Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(376,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.376");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.bt (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(54\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 571.26 | ||
Character | \(\chi\) | \(=\) | 585.571 |
Dual form | 585.2.bt.b.376.26 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.146304 | + | 0.0844686i | −0.103452 | + | 0.0597283i | −0.550834 | − | 0.834615i | \(-0.685690\pi\) |
0.447381 | + | 0.894343i | \(0.352357\pi\) | |||||||
\(3\) | −0.106608 | − | 1.72877i | −0.0615502 | − | 0.998104i | ||||
\(4\) | −0.985730 | + | 1.70733i | −0.492865 | + | 0.853667i | ||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | 0.161624 | + | 0.243920i | 0.0659826 | + | 0.0995801i | ||||
\(7\) | −1.65898 | + | 0.957814i | −0.627037 | + | 0.362020i | −0.779604 | − | 0.626273i | \(-0.784579\pi\) |
0.152567 | + | 0.988293i | \(0.451246\pi\) | |||||||
\(8\) | − | 0.670927i | − | 0.237209i | ||||||
\(9\) | −2.97727 | + | 0.368601i | −0.992423 | + | 0.122867i | ||||
\(10\) | −0.168937 | −0.0534226 | ||||||||
\(11\) | 3.52392 | − | 2.03454i | 1.06250 | − | 0.613436i | 0.136380 | − | 0.990657i | \(-0.456453\pi\) |
0.926124 | + | 0.377220i | \(0.123120\pi\) | |||||||
\(12\) | 3.05667 | + | 1.52208i | 0.882385 | + | 0.439387i | ||||
\(13\) | 1.15689 | + | 3.41491i | 0.320863 | + | 0.947126i | ||||
\(14\) | 0.161810 | − | 0.280264i | 0.0432457 | − | 0.0749037i | ||||
\(15\) | 0.772058 | − | 1.55046i | 0.199345 | − | 0.400327i | ||||
\(16\) | −1.91479 | − | 3.31651i | −0.478697 | − | 0.829127i | ||||
\(17\) | −0.709628 | −0.172110 | −0.0860550 | − | 0.996290i | \(-0.527426\pi\) | ||||
−0.0860550 | + | 0.996290i | \(0.527426\pi\) | |||||||
\(18\) | 0.404451 | − | 0.305414i | 0.0953300 | − | 0.0719867i | ||||
\(19\) | 6.45837i | 1.48165i | 0.671697 | + | 0.740826i | \(0.265565\pi\) | ||||
−0.671697 | + | 0.740826i | \(0.734435\pi\) | |||||||
\(20\) | −1.70733 | + | 0.985730i | −0.381772 | + | 0.220416i | ||||
\(21\) | 1.83270 | + | 2.76588i | 0.399928 | + | 0.603565i | ||||
\(22\) | −0.343709 | + | 0.595322i | −0.0732791 | + | 0.126923i | ||||
\(23\) | −4.18851 | + | 7.25472i | −0.873365 | + | 1.51271i | −0.0148717 | + | 0.999889i | \(0.504734\pi\) |
−0.858494 | + | 0.512824i | \(0.828599\pi\) | |||||||
\(24\) | −1.15988 | + | 0.0715262i | −0.236759 | + | 0.0146002i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | −0.457710 | − | 0.401894i | −0.0897643 | − | 0.0788179i | ||||
\(27\) | 0.954626 | + | 5.10771i | 0.183718 | + | 0.982979i | ||||
\(28\) | − | 3.77659i | − | 0.713708i | ||||||
\(29\) | 3.53514 | + | 6.12304i | 0.656459 | + | 1.13702i | 0.981526 | + | 0.191329i | \(0.0612798\pi\) |
−0.325067 | + | 0.945691i | \(0.605387\pi\) | |||||||
\(30\) | 0.0180101 | + | 0.292053i | 0.00328817 | + | 0.0533214i | ||||
\(31\) | 4.30244 | + | 2.48401i | 0.772741 | + | 0.446142i | 0.833851 | − | 0.551989i | \(-0.186131\pi\) |
−0.0611108 | + | 0.998131i | \(0.519464\pi\) | |||||||
\(32\) | 1.72236 | + | 0.994406i | 0.304474 | + | 0.175788i | ||||
\(33\) | −3.89292 | − | 5.87515i | −0.677671 | − | 1.02273i | ||||
\(34\) | 0.103821 | − | 0.0599413i | 0.0178052 | − | 0.0102798i | ||||
\(35\) | −1.91563 | −0.323800 | ||||||||
\(36\) | 2.30546 | − | 5.44654i | 0.384243 | − | 0.907756i | ||||
\(37\) | − | 5.73681i | − | 0.943125i | −0.881833 | − | 0.471563i | \(-0.843690\pi\) | ||
0.881833 | − | 0.471563i | \(-0.156310\pi\) | |||||||
\(38\) | −0.545529 | − | 0.944885i | −0.0884965 | − | 0.153281i | ||||
\(39\) | 5.78025 | − | 2.36404i | 0.925581 | − | 0.378550i | ||||
\(40\) | 0.335464 | − | 0.581040i | 0.0530415 | − | 0.0918705i | ||||
\(41\) | 9.47008 | + | 5.46755i | 1.47898 | + | 0.853888i | 0.999717 | − | 0.0237844i | \(-0.00757151\pi\) |
0.479261 | + | 0.877673i | \(0.340905\pi\) | |||||||
\(42\) | −0.501761 | − | 0.249854i | −0.0774235 | − | 0.0385533i | ||||
\(43\) | −4.35016 | − | 7.53470i | −0.663393 | − | 1.14903i | −0.979718 | − | 0.200379i | \(-0.935782\pi\) |
0.316325 | − | 0.948651i | \(-0.397551\pi\) | |||||||
\(44\) | 8.02202i | 1.20937i | ||||||||
\(45\) | −2.76269 | − | 1.16942i | −0.411838 | − | 0.174326i | ||||
\(46\) | − | 1.41519i | − | 0.208659i | ||||||
\(47\) | 2.97238 | − | 1.71611i | 0.433567 | − | 0.250320i | −0.267298 | − | 0.963614i | \(-0.586131\pi\) |
0.700865 | + | 0.713294i | \(0.252798\pi\) | |||||||
\(48\) | −5.52934 | + | 3.66379i | −0.798092 | + | 0.528822i | ||||
\(49\) | −1.66518 | + | 2.88418i | −0.237883 | + | 0.412026i | ||||
\(50\) | −0.146304 | − | 0.0844686i | −0.0206905 | − | 0.0119457i | ||||
\(51\) | 0.0756520 | + | 1.22678i | 0.0105934 | + | 0.171784i | ||||
\(52\) | −6.97077 | − | 1.39099i | −0.966672 | − | 0.192895i | ||||
\(53\) | 1.83872 | 0.252567 | 0.126283 | − | 0.991994i | \(-0.459695\pi\) | ||||
0.126283 | + | 0.991994i | \(0.459695\pi\) | |||||||
\(54\) | −0.571107 | − | 0.666642i | −0.0777178 | − | 0.0907185i | ||||
\(55\) | 4.06908 | 0.548674 | ||||||||
\(56\) | 0.642624 | + | 1.11306i | 0.0858742 | + | 0.148739i | ||||
\(57\) | 11.1650 | − | 0.688514i | 1.47884 | − | 0.0911959i | ||||
\(58\) | −1.03441 | − | 0.597217i | −0.135825 | − | 0.0784184i | ||||
\(59\) | −8.61560 | − | 4.97422i | −1.12166 | − | 0.647588i | −0.179832 | − | 0.983697i | \(-0.557555\pi\) |
−0.941823 | + | 0.336109i | \(0.890889\pi\) | |||||||
\(60\) | 1.88611 | + | 2.84650i | 0.243496 | + | 0.367481i | ||||
\(61\) | 1.50640 | + | 2.60916i | 0.192874 | + | 0.334068i | 0.946202 | − | 0.323578i | \(-0.104886\pi\) |
−0.753327 | + | 0.657646i | \(0.771552\pi\) | |||||||
\(62\) | −0.839285 | −0.106589 | ||||||||
\(63\) | 4.58619 | − | 3.46317i | 0.577805 | − | 0.436319i | ||||
\(64\) | 7.32317 | 0.915396 | ||||||||
\(65\) | −0.705562 | + | 3.53584i | −0.0875142 | + | 0.438567i | ||||
\(66\) | 1.06582 | + | 0.530727i | 0.131193 | + | 0.0653280i | ||||
\(67\) | −3.37333 | − | 1.94759i | −0.412118 | − | 0.237936i | 0.279581 | − | 0.960122i | \(-0.409804\pi\) |
−0.691699 | + | 0.722186i | \(0.743138\pi\) | |||||||
\(68\) | 0.699502 | − | 1.21157i | 0.0848270 | − | 0.146925i | ||||
\(69\) | 12.9882 | + | 6.46755i | 1.56360 | + | 0.778602i | ||||
\(70\) | 0.280264 | − | 0.161810i | 0.0334980 | − | 0.0193401i | ||||
\(71\) | 5.70024i | 0.676494i | 0.941057 | + | 0.338247i | \(0.109834\pi\) | ||||
−0.941057 | + | 0.338247i | \(0.890166\pi\) | |||||||
\(72\) | 0.247304 | + | 1.99753i | 0.0291451 | + | 0.235411i | ||||
\(73\) | 5.79311i | 0.678032i | 0.940781 | + | 0.339016i | \(0.110094\pi\) | ||||
−0.940781 | + | 0.339016i | \(0.889906\pi\) | |||||||
\(74\) | 0.484580 | + | 0.839317i | 0.0563313 | + | 0.0975687i | ||||
\(75\) | 1.44385 | − | 0.956709i | 0.166722 | − | 0.110471i | ||||
\(76\) | −11.0266 | − | 6.36621i | −1.26484 | − | 0.730254i | ||||
\(77\) | −3.89742 | + | 6.75053i | −0.444152 | + | 0.769294i | ||||
\(78\) | −0.645986 | + | 0.834119i | −0.0731435 | + | 0.0944453i | ||||
\(79\) | −6.92507 | − | 11.9946i | −0.779131 | − | 1.34949i | −0.932443 | − | 0.361317i | \(-0.882327\pi\) |
0.153312 | − | 0.988178i | \(-0.451006\pi\) | |||||||
\(80\) | − | 3.82958i | − | 0.428160i | ||||||
\(81\) | 8.72827 | − | 2.19485i | 0.969807 | − | 0.243872i | ||||
\(82\) | −1.84735 | −0.204005 | ||||||||
\(83\) | 3.02842 | − | 1.74846i | 0.332412 | − | 0.191918i | −0.324499 | − | 0.945886i | \(-0.605196\pi\) |
0.656911 | + | 0.753968i | \(0.271863\pi\) | |||||||
\(84\) | −6.52884 | + | 0.402614i | −0.712354 | + | 0.0439288i | ||||
\(85\) | −0.614556 | − | 0.354814i | −0.0666579 | − | 0.0384850i | ||||
\(86\) | 1.27289 | + | 0.734904i | 0.137259 | + | 0.0792467i | ||||
\(87\) | 10.2084 | − | 6.76420i | 1.09446 | − | 0.725198i | ||||
\(88\) | −1.36503 | − | 2.36430i | −0.145512 | − | 0.252035i | ||||
\(89\) | 10.0932i | 1.06987i | 0.844892 | + | 0.534937i | \(0.179665\pi\) | ||||
−0.844892 | + | 0.534937i | \(0.820335\pi\) | |||||||
\(90\) | 0.502972 | − | 0.0622704i | 0.0530179 | − | 0.00656388i | ||||
\(91\) | −5.19011 | − | 4.55720i | −0.544071 | − | 0.477724i | ||||
\(92\) | −8.25749 | − | 14.3024i | −0.860903 | − | 1.49113i | ||||
\(93\) | 3.83561 | − | 7.70273i | 0.397734 | − | 0.798736i | ||||
\(94\) | −0.289914 | + | 0.502146i | −0.0299024 | + | 0.0517924i | ||||
\(95\) | −3.22918 | + | 5.59311i | −0.331307 | + | 0.573841i | ||||
\(96\) | 1.53548 | − | 3.08357i | 0.156714 | − | 0.314716i | ||||
\(97\) | −14.5254 | + | 8.38627i | −1.47484 | + | 0.851497i | −0.999598 | − | 0.0283603i | \(-0.990971\pi\) |
−0.475238 | + | 0.879857i | \(0.657638\pi\) | |||||||
\(98\) | − | 0.562623i | − | 0.0568335i | ||||||
\(99\) | −9.74174 | + | 7.35629i | −0.979082 | + | 0.739335i | ||||
\(100\) | −1.97146 | −0.197146 | ||||||||
\(101\) | −3.49270 | − | 6.04953i | −0.347536 | − | 0.601951i | 0.638275 | − | 0.769809i | \(-0.279648\pi\) |
−0.985811 | + | 0.167858i | \(0.946315\pi\) | |||||||
\(102\) | −0.114693 | − | 0.173093i | −0.0113563 | − | 0.0171387i | ||||
\(103\) | 7.02176 | − | 12.1620i | 0.691875 | − | 1.19836i | −0.279348 | − | 0.960190i | \(-0.590118\pi\) |
0.971223 | − | 0.238172i | \(-0.0765483\pi\) | |||||||
\(104\) | 2.29116 | − | 0.776187i | 0.224666 | − | 0.0761114i | ||||
\(105\) | 0.204221 | + | 3.31167i | 0.0199300 | + | 0.323186i | ||||
\(106\) | −0.269011 | + | 0.155314i | −0.0261287 | + | 0.0150854i | ||||
\(107\) | −7.11099 | −0.687445 | −0.343723 | − | 0.939071i | \(-0.611688\pi\) | ||||
−0.343723 | + | 0.939071i | \(0.611688\pi\) | |||||||
\(108\) | −9.66157 | − | 3.40496i | −0.929685 | − | 0.327642i | ||||
\(109\) | − | 14.0348i | − | 1.34429i | −0.740420 | − | 0.672145i | \(-0.765373\pi\) | ||
0.740420 | − | 0.672145i | \(-0.234627\pi\) | |||||||
\(110\) | −0.595322 | + | 0.343709i | −0.0567617 | + | 0.0327714i | ||||
\(111\) | −9.91760 | + | 0.611590i | −0.941337 | + | 0.0580495i | ||||
\(112\) | 6.35320 | + | 3.66802i | 0.600321 | + | 0.346596i | ||||
\(113\) | −2.53374 | + | 4.38856i | −0.238354 | + | 0.412841i | −0.960242 | − | 0.279169i | \(-0.909941\pi\) |
0.721888 | + | 0.692010i | \(0.243274\pi\) | |||||||
\(114\) | −1.57533 | + | 1.04383i | −0.147543 | + | 0.0977632i | ||||
\(115\) | −7.25472 | + | 4.18851i | −0.676506 | + | 0.390581i | ||||
\(116\) | −13.9388 | −1.29418 | ||||||||
\(117\) | −4.70310 | − | 9.74068i | −0.434802 | − | 0.900526i | ||||
\(118\) | 1.68066 | 0.154717 | ||||||||
\(119\) | 1.17726 | − | 0.679692i | 0.107919 | − | 0.0623072i | ||||
\(120\) | −1.04025 | − | 0.517995i | −0.0949611 | − | 0.0472863i | ||||
\(121\) | 2.77869 | − | 4.81284i | 0.252609 | − | 0.437531i | ||||
\(122\) | −0.440784 | − | 0.254487i | −0.0399067 | − | 0.0230401i | ||||
\(123\) | 8.44254 | − | 16.9544i | 0.761238 | − | 1.52873i | ||||
\(124\) | −8.48208 | + | 4.89713i | −0.761714 | + | 0.439776i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −0.378448 | + | 0.894065i | −0.0337148 | + | 0.0796496i | ||||
\(127\) | 8.64652 | 0.767255 | 0.383627 | − | 0.923488i | \(-0.374675\pi\) | ||||
0.383627 | + | 0.923488i | \(0.374675\pi\) | |||||||
\(128\) | −4.51613 | + | 2.60739i | −0.399174 | + | 0.230463i | ||||
\(129\) | −12.5620 | + | 8.32367i | −1.10602 | + | 0.732858i | ||||
\(130\) | −0.195441 | − | 0.576905i | −0.0171413 | − | 0.0505980i | ||||
\(131\) | 2.38004 | − | 4.12236i | 0.207945 | − | 0.360172i | −0.743122 | − | 0.669156i | \(-0.766656\pi\) |
0.951067 | + | 0.308984i | \(0.0999890\pi\) | |||||||
\(132\) | 13.8682 | − | 0.855212i | 1.20707 | − | 0.0744366i | ||||
\(133\) | −6.18592 | − | 10.7143i | −0.536387 | − | 0.929049i | ||||
\(134\) | 0.658042 | 0.0568462 | ||||||||
\(135\) | −1.72712 | + | 4.90072i | −0.148647 | + | 0.421787i | ||||
\(136\) | 0.476109i | 0.0408260i | ||||||||
\(137\) | 8.86562 | − | 5.11857i | 0.757441 | − | 0.437309i | −0.0709354 | − | 0.997481i | \(-0.522598\pi\) |
0.828376 | + | 0.560172i | \(0.189265\pi\) | |||||||
\(138\) | −2.44654 | + | 0.150871i | −0.208263 | + | 0.0128430i | ||||
\(139\) | 5.77777 | − | 10.0074i | 0.490064 | − | 0.848816i | −0.509871 | − | 0.860251i | \(-0.670307\pi\) |
0.999935 | + | 0.0114355i | \(0.00364012\pi\) | |||||||
\(140\) | 1.88829 | − | 3.27062i | 0.159590 | − | 0.276418i | ||||
\(141\) | −3.28363 | − | 4.95561i | −0.276531 | − | 0.417337i | ||||
\(142\) | −0.481491 | − | 0.833967i | −0.0404059 | − | 0.0699850i | ||||
\(143\) | 11.0245 | + | 9.68015i | 0.921919 | + | 0.809495i | ||||
\(144\) | 6.92331 | + | 9.16835i | 0.576942 | + | 0.764029i | ||||
\(145\) | 7.07028i | 0.587155i | ||||||||
\(146\) | −0.489336 | − | 0.847555i | −0.0404977 | − | 0.0701441i | ||||
\(147\) | 5.16360 | + | 2.57124i | 0.425887 | + | 0.212072i | ||||
\(148\) | 9.79465 | + | 5.65494i | 0.805115 | + | 0.464833i | ||||
\(149\) | 19.0393 | + | 10.9923i | 1.55976 | + | 0.900526i | 0.997279 | + | 0.0737131i | \(0.0234849\pi\) |
0.562477 | + | 0.826813i | \(0.309848\pi\) | |||||||
\(150\) | −0.130429 | + | 0.261930i | −0.0106495 | + | 0.0213865i | ||||
\(151\) | 0.201741 | − | 0.116475i | 0.0164175 | − | 0.00947862i | −0.491769 | − | 0.870726i | \(-0.663649\pi\) |
0.508186 | + | 0.861247i | \(0.330316\pi\) | |||||||
\(152\) | 4.33310 | 0.351461 | ||||||||
\(153\) | 2.11275 | − | 0.261569i | 0.170806 | − | 0.0211466i | ||||
\(154\) | − | 1.31684i | − | 0.106114i | ||||||
\(155\) | 2.48401 | + | 4.30244i | 0.199521 | + | 0.345580i | ||||
\(156\) | −1.66155 | + | 12.1991i | −0.133031 | + | 0.976712i | ||||
\(157\) | −10.2882 | + | 17.8197i | −0.821087 | + | 1.42216i | 0.0837862 | + | 0.996484i | \(0.473299\pi\) |
−0.904873 | + | 0.425681i | \(0.860035\pi\) | |||||||
\(158\) | 2.02633 | + | 1.16990i | 0.161206 | + | 0.0930724i | ||||
\(159\) | −0.196022 | − | 3.17871i | −0.0155455 | − | 0.252088i | ||||
\(160\) | 0.994406 | + | 1.72236i | 0.0786147 | + | 0.136165i | ||||
\(161\) | − | 16.0473i | − | 1.26470i | ||||||
\(162\) | −1.09158 | + | 1.05838i | −0.0857629 | + | 0.0831541i | ||||
\(163\) | − | 15.6276i | − | 1.22404i | −0.790841 | − | 0.612022i | \(-0.790356\pi\) | ||
0.790841 | − | 0.612022i | \(-0.209644\pi\) | |||||||
\(164\) | −18.6699 | + | 10.7791i | −1.45787 | + | 0.841703i | ||||
\(165\) | −0.433796 | − | 7.03449i | −0.0337710 | − | 0.547634i | ||||
\(166\) | −0.295380 | + | 0.511612i | −0.0229259 | + | 0.0397088i | ||||
\(167\) | −8.64820 | − | 4.99304i | −0.669218 | − | 0.386373i | 0.126563 | − | 0.991959i | \(-0.459606\pi\) |
−0.795780 | + | 0.605586i | \(0.792939\pi\) | |||||||
\(168\) | 1.85571 | − | 1.22961i | 0.143171 | − | 0.0948663i | ||||
\(169\) | −10.3232 | + | 7.90133i | −0.794094 | + | 0.607795i | ||||
\(170\) | 0.119883 | 0.00919457 | ||||||||
\(171\) | −2.38056 | − | 19.2283i | −0.182046 | − | 1.47042i | ||||
\(172\) | 17.1523 | 1.30785 | ||||||||
\(173\) | −8.04100 | − | 13.9274i | −0.611346 | − | 1.05888i | −0.991014 | − | 0.133759i | \(-0.957295\pi\) |
0.379668 | − | 0.925123i | \(-0.376038\pi\) | |||||||
\(174\) | −0.922172 | + | 1.85192i | −0.0699097 | + | 0.140394i | ||||
\(175\) | −1.65898 | − | 0.957814i | −0.125407 | − | 0.0724040i | ||||
\(176\) | −13.4951 | − | 7.79142i | −1.01723 | − | 0.587300i | ||||
\(177\) | −7.68077 | + | 15.4246i | −0.577322 | + | 1.15939i | ||||
\(178\) | −0.852557 | − | 1.47667i | −0.0639018 | − | 0.110681i | ||||
\(179\) | 6.68173 | 0.499416 | 0.249708 | − | 0.968321i | \(-0.419665\pi\) | ||||
0.249708 | + | 0.968321i | \(0.419665\pi\) | |||||||
\(180\) | 4.71985 | − | 3.56411i | 0.351797 | − | 0.265653i | ||||
\(181\) | −12.1819 | −0.905474 | −0.452737 | − | 0.891644i | \(-0.649552\pi\) | ||||
−0.452737 | + | 0.891644i | \(0.649552\pi\) | |||||||
\(182\) | 1.14427 | + | 0.228335i | 0.0848191 | + | 0.0169253i | ||||
\(183\) | 4.35003 | − | 2.88237i | 0.321563 | − | 0.213071i | ||||
\(184\) | 4.86739 | + | 2.81019i | 0.358829 | + | 0.207170i | ||||
\(185\) | 2.86840 | − | 4.96822i | 0.210889 | − | 0.365271i | ||||
\(186\) | 0.0894745 | + | 1.45093i | 0.00656059 | + | 0.106387i | ||||
\(187\) | −2.50068 | + | 1.44377i | −0.182867 | + | 0.105579i | ||||
\(188\) | 6.76647i | 0.493496i | ||||||||
\(189\) | −6.47594 | − | 7.55925i | −0.471056 | − | 0.549854i | ||||
\(190\) | − | 1.09106i | − | 0.0791537i | ||||||
\(191\) | 8.26341 | + | 14.3126i | 0.597919 | + | 1.03563i | 0.993128 | + | 0.117035i | \(0.0373390\pi\) |
−0.395209 | + | 0.918591i | \(0.629328\pi\) | |||||||
\(192\) | −0.780708 | − | 12.6600i | −0.0563428 | − | 0.913660i | ||||
\(193\) | 12.4581 | + | 7.19271i | 0.896757 | + | 0.517743i | 0.876147 | − | 0.482045i | \(-0.160106\pi\) |
0.0206103 | + | 0.999788i | \(0.493439\pi\) | |||||||
\(194\) | 1.41675 | − | 2.45389i | 0.101717 | − | 0.176179i | ||||
\(195\) | 6.18787 | + | 0.842803i | 0.443122 | + | 0.0603544i | ||||
\(196\) | −3.28284 | − | 5.68605i | −0.234489 | − | 0.406147i | ||||
\(197\) | − | 24.7703i | − | 1.76481i | −0.470489 | − | 0.882406i | \(-0.655922\pi\) | ||
0.470489 | − | 0.882406i | \(-0.344078\pi\) | |||||||
\(198\) | 0.803879 | − | 1.89913i | 0.0571292 | − | 0.134965i | ||||
\(199\) | 9.54246 | 0.676447 | 0.338224 | − | 0.941066i | \(-0.390174\pi\) | ||||
0.338224 | + | 0.941066i | \(0.390174\pi\) | |||||||
\(200\) | 0.581040 | − | 0.335464i | 0.0410857 | − | 0.0237209i | ||||
\(201\) | −3.00731 | + | 6.03933i | −0.212119 | + | 0.425982i | ||||
\(202\) | 1.02199 | + | 0.590047i | 0.0719070 | + | 0.0415155i | ||||
\(203\) | −11.7295 | − | 6.77201i | −0.823247 | − | 0.475302i | ||||
\(204\) | −2.16910 | − | 1.08011i | −0.151867 | − | 0.0756230i | ||||
\(205\) | 5.46755 | + | 9.47008i | 0.381870 | + | 0.661419i | ||||
\(206\) | 2.37247i | 0.165298i | ||||||||
\(207\) | 9.79624 | − | 23.1431i | 0.680886 | − | 1.60856i | ||||
\(208\) | 9.11039 | − | 10.3757i | 0.631692 | − | 0.719422i | ||||
\(209\) | 13.1398 | + | 22.7588i | 0.908899 | + | 1.57426i | ||||
\(210\) | −0.309611 | − | 0.467261i | −0.0213652 | − | 0.0322441i | ||||
\(211\) | −4.51728 | + | 7.82415i | −0.310982 | + | 0.538637i | −0.978575 | − | 0.205889i | \(-0.933991\pi\) |
0.667593 | + | 0.744526i | \(0.267325\pi\) | |||||||
\(212\) | −1.81248 | + | 3.13930i | −0.124481 | + | 0.215608i | ||||
\(213\) | 9.85438 | − | 0.607691i | 0.675211 | − | 0.0416383i | ||||
\(214\) | 1.04037 | − | 0.600656i | 0.0711180 | − | 0.0410600i | ||||
\(215\) | − | 8.70032i | − | 0.593357i | ||||||
\(216\) | 3.42690 | − | 0.640485i | 0.233171 | − | 0.0435795i | ||||
\(217\) | −9.51689 | −0.646049 | ||||||||
\(218\) | 1.18550 | + | 2.05335i | 0.0802921 | + | 0.139070i | ||||
\(219\) | 10.0149 | − | 0.617592i | 0.676747 | − | 0.0417330i | ||||
\(220\) | −4.01101 | + | 6.94728i | −0.270422 | + | 0.468385i | ||||
\(221\) | −0.820959 | − | 2.42332i | −0.0552237 | − | 0.163010i | ||||
\(222\) | 1.39932 | − | 0.927204i | 0.0939165 | − | 0.0622299i | ||||
\(223\) | 12.8944 | − | 7.44457i | 0.863471 | − | 0.498525i | −0.00170200 | − | 0.999999i | \(-0.500542\pi\) |
0.865173 | + | 0.501473i | \(0.167208\pi\) | |||||||
\(224\) | −3.80983 | −0.254555 | ||||||||
\(225\) | −1.80785 | − | 2.39409i | −0.120523 | − | 0.159606i | ||||
\(226\) | − | 0.856085i | − | 0.0569459i | ||||||
\(227\) | 14.1677 | − | 8.17971i | 0.940341 | − | 0.542906i | 0.0502738 | − | 0.998735i | \(-0.483991\pi\) |
0.890067 | + | 0.455829i | \(0.150657\pi\) | |||||||
\(228\) | −9.83016 | + | 19.7411i | −0.651019 | + | 1.30739i | ||||
\(229\) | 2.01410 | + | 1.16284i | 0.133096 | + | 0.0768427i | 0.565069 | − | 0.825043i | \(-0.308849\pi\) |
−0.431974 | + | 0.901886i | \(0.642183\pi\) | |||||||
\(230\) | 0.707596 | − | 1.22559i | 0.0466575 | − | 0.0808131i | ||||
\(231\) | 12.0856 | + | 6.01807i | 0.795173 | + | 0.395960i | ||||
\(232\) | 4.10812 | − | 2.37182i | 0.269711 | − | 0.155718i | ||||
\(233\) | −8.48290 | −0.555733 | −0.277867 | − | 0.960620i | \(-0.589627\pi\) | ||||
−0.277867 | + | 0.960620i | \(0.589627\pi\) | |||||||
\(234\) | 1.51086 | + | 1.02784i | 0.0987683 | + | 0.0671917i | ||||
\(235\) | 3.43221 | 0.223893 | ||||||||
\(236\) | 16.9853 | − | 9.80647i | 1.10565 | − | 0.638347i | ||||
\(237\) | −19.9975 | + | 13.2505i | −1.29898 | + | 0.860715i | ||||
\(238\) | −0.114825 | + | 0.198883i | −0.00744302 | + | 0.0128917i | ||||
\(239\) | 7.83208 | + | 4.52185i | 0.506615 | + | 0.292494i | 0.731441 | − | 0.681905i | \(-0.238848\pi\) |
−0.224826 | + | 0.974399i | \(0.572181\pi\) | |||||||
\(240\) | −6.62044 | + | 0.408263i | −0.427348 | + | 0.0263533i | ||||
\(241\) | 7.31598 | − | 4.22388i | 0.471264 | − | 0.272084i | −0.245505 | − | 0.969395i | \(-0.578954\pi\) |
0.716769 | + | 0.697311i | \(0.245620\pi\) | |||||||
\(242\) | 0.938850i | 0.0603516i | ||||||||
\(243\) | −4.72488 | − | 14.8551i | −0.303101 | − | 0.952958i | ||||
\(244\) | −5.93961 | −0.380244 | ||||||||
\(245\) | −2.88418 | + | 1.66518i | −0.184264 | + | 0.106385i | ||||
\(246\) | 0.196942 | + | 3.19363i | 0.0125566 | + | 0.203618i | ||||
\(247\) | −22.0547 | + | 7.47160i | −1.40331 | + | 0.475407i | ||||
\(248\) | 1.66659 | − | 2.88662i | 0.105829 | − | 0.183301i | ||||
\(249\) | −3.34553 | − | 5.04903i | −0.212014 | − | 0.319969i | ||||
\(250\) | −0.0844686 | − | 0.146304i | −0.00534226 | − | 0.00925307i | ||||
\(251\) | 5.17089 | 0.326384 | 0.163192 | − | 0.986594i | \(-0.447821\pi\) | ||||
0.163192 | + | 0.986594i | \(0.447821\pi\) | |||||||
\(252\) | 1.39205 | + | 11.2439i | 0.0876911 | + | 0.708300i | ||||
\(253\) | 34.0868i | 2.14302i | ||||||||
\(254\) | −1.26502 | + | 0.730360i | −0.0793744 | + | 0.0458269i | ||||
\(255\) | −0.547874 | + | 1.10025i | −0.0343092 | + | 0.0689003i | ||||
\(256\) | −6.88268 | + | 11.9212i | −0.430168 | + | 0.745072i | ||||
\(257\) | 4.09728 | − | 7.09669i | 0.255581 | − | 0.442679i | −0.709472 | − | 0.704734i | \(-0.751067\pi\) |
0.965053 | + | 0.262054i | \(0.0843999\pi\) | |||||||
\(258\) | 1.13478 | − | 2.27888i | 0.0706481 | − | 0.141877i | ||||
\(259\) | 5.49480 | + | 9.51726i | 0.341430 | + | 0.591374i | ||||
\(260\) | −5.34137 | − | 4.69002i | −0.331258 | − | 0.290862i | ||||
\(261\) | −12.7820 | − | 16.9269i | −0.791187 | − | 1.04775i | ||||
\(262\) | 0.804156i | 0.0496809i | ||||||||
\(263\) | 6.89246 | + | 11.9381i | 0.425008 | + | 0.736135i | 0.996421 | − | 0.0845276i | \(-0.0269381\pi\) |
−0.571414 | + | 0.820662i | \(0.693605\pi\) | |||||||
\(264\) | −3.94180 | + | 2.61187i | −0.242601 | + | 0.160749i | ||||
\(265\) | 1.59237 | + | 0.919358i | 0.0978188 | + | 0.0564757i | ||||
\(266\) | 1.81005 | + | 1.04503i | 0.110981 | + | 0.0640750i | ||||
\(267\) | 17.4488 | − | 1.07601i | 1.06785 | − | 0.0658510i | ||||
\(268\) | 6.65039 | − | 3.83960i | 0.406237 | − | 0.234541i | ||||
\(269\) | 16.6922 | 1.01774 | 0.508872 | − | 0.860842i | \(-0.330063\pi\) | ||||
0.508872 | + | 0.860842i | \(0.330063\pi\) | |||||||
\(270\) | −0.161272 | − | 0.862882i | −0.00981469 | − | 0.0525133i | ||||
\(271\) | 1.35107i | 0.0820715i | 0.999158 | + | 0.0410358i | \(0.0130658\pi\) | ||||
−0.999158 | + | 0.0410358i | \(0.986934\pi\) | |||||||
\(272\) | 1.35879 | + | 2.35349i | 0.0823886 | + | 0.142701i | ||||
\(273\) | −7.32502 | + | 9.45832i | −0.443330 | + | 0.572443i | ||||
\(274\) | −0.864716 | + | 1.49773i | −0.0522394 | + | 0.0904813i | ||||
\(275\) | 3.52392 | + | 2.03454i | 0.212501 | + | 0.122687i | ||||
\(276\) | −23.8452 | + | 15.8000i | −1.43531 | + | 0.951049i | ||||
\(277\) | 3.98598 | + | 6.90392i | 0.239494 | + | 0.414817i | 0.960569 | − | 0.278041i | \(-0.0896850\pi\) |
−0.721075 | + | 0.692857i | \(0.756352\pi\) | |||||||
\(278\) | 1.95216i | 0.117083i | ||||||||
\(279\) | −13.7251 | − | 5.80970i | −0.821702 | − | 0.347817i | ||||
\(280\) | 1.28525i | 0.0768082i | ||||||||
\(281\) | −21.0588 | + | 12.1583i | −1.25626 | + | 0.725304i | −0.972346 | − | 0.233545i | \(-0.924967\pi\) |
−0.283917 | + | 0.958849i | \(0.591634\pi\) | |||||||
\(282\) | 0.899001 | + | 0.447661i | 0.0535347 | + | 0.0266578i | ||||
\(283\) | −7.68858 | + | 13.3170i | −0.457039 | + | 0.791615i | −0.998803 | − | 0.0489160i | \(-0.984423\pi\) |
0.541764 | + | 0.840531i | \(0.317757\pi\) | |||||||
\(284\) | −9.73222 | − | 5.61890i | −0.577501 | − | 0.333420i | ||||
\(285\) | 10.0134 | + | 4.98624i | 0.593145 | + | 0.295359i | ||||
\(286\) | −2.43060 | − | 0.485016i | −0.143725 | − | 0.0286796i | ||||
\(287\) | −20.9476 | −1.23650 | ||||||||
\(288\) | −5.49448 | − | 2.32575i | −0.323765 | − | 0.137046i | ||||
\(289\) | −16.4964 | −0.970378 | ||||||||
\(290\) | −0.597217 | − | 1.03441i | −0.0350698 | − | 0.0607426i | ||||
\(291\) | 16.0464 | + | 24.2171i | 0.940659 | + | 1.41963i | ||||
\(292\) | −9.89078 | − | 5.71044i | −0.578814 | − | 0.334178i | ||||
\(293\) | 17.2223 | + | 9.94332i | 1.00614 | + | 0.580895i | 0.910059 | − | 0.414479i | \(-0.136036\pi\) |
0.0960804 | + | 0.995374i | \(0.469369\pi\) | |||||||
\(294\) | −0.972644 | + | 0.0599801i | −0.0567258 | + | 0.00349811i | ||||
\(295\) | −4.97422 | − | 8.61560i | −0.289610 | − | 0.501619i | ||||
\(296\) | −3.84898 | −0.223718 | ||||||||
\(297\) | 13.7559 | + | 16.0570i | 0.798196 | + | 0.931719i | ||||
\(298\) | −3.71402 | −0.215148 | ||||||||
\(299\) | −29.6198 | − | 5.91051i | −1.71296 | − | 0.341814i | ||||
\(300\) | 0.210173 | + | 3.40820i | 0.0121344 | + | 0.196772i | ||||
\(301\) | 14.4337 | + | 8.33329i | 0.831943 | + | 0.480323i | ||||
\(302\) | −0.0196770 | + | 0.0340816i | −0.00113228 | + | 0.00196117i | ||||
\(303\) | −10.0859 | + | 6.68299i | −0.579418 | + | 0.383928i | ||||
\(304\) | 21.4192 | − | 12.3664i | 1.22848 | − | 0.709262i | ||||
\(305\) | 3.01280i | 0.172512i | ||||||||
\(306\) | −0.287010 | + | 0.216730i | −0.0164073 | + | 0.0123896i | ||||
\(307\) | − | 2.04562i | − | 0.116750i | −0.998295 | − | 0.0583750i | \(-0.981408\pi\) | ||
0.998295 | − | 0.0583750i | \(-0.0185919\pi\) | |||||||
\(308\) | −7.68361 | − | 13.3084i | −0.437814 | − | 0.758316i | ||||
\(309\) | −21.7739 | − | 10.8424i | −1.23868 | − | 0.616804i | ||||
\(310\) | −0.726842 | − | 0.419642i | −0.0412818 | − | 0.0238341i | ||||
\(311\) | 11.3301 | − | 19.6243i | 0.642471 | − | 1.11279i | −0.342408 | − | 0.939551i | \(-0.611243\pi\) |
0.984879 | − | 0.173241i | \(-0.0554241\pi\) | |||||||
\(312\) | −1.58610 | − | 3.87813i | −0.0897954 | − | 0.219556i | ||||
\(313\) | 3.88016 | + | 6.72064i | 0.219320 | + | 0.379873i | 0.954600 | − | 0.297890i | \(-0.0962829\pi\) |
−0.735280 | + | 0.677763i | \(0.762950\pi\) | |||||||
\(314\) | − | 3.47612i | − | 0.196169i | ||||||
\(315\) | 5.70334 | − | 0.706102i | 0.321347 | − | 0.0397843i | ||||
\(316\) | 27.3050 | 1.53603 | ||||||||
\(317\) | 4.17572 | − | 2.41085i | 0.234532 | − | 0.135407i | −0.378129 | − | 0.925753i | \(-0.623432\pi\) |
0.612661 | + | 0.790346i | \(0.290099\pi\) | |||||||
\(318\) | 0.297180 | + | 0.448500i | 0.0166650 | + | 0.0251506i | ||||
\(319\) | 24.9151 | + | 14.3848i | 1.39498 | + | 0.805392i | ||||
\(320\) | 6.34205 | + | 3.66158i | 0.354531 | + | 0.204689i | ||||
\(321\) | 0.758089 | + | 12.2932i | 0.0423124 | + | 0.686142i | ||||
\(322\) | 1.35549 | + | 2.34778i | 0.0755385 | + | 0.130837i | ||||
\(323\) | − | 4.58304i | − | 0.255007i | ||||||
\(324\) | −4.85638 | + | 17.0656i | −0.269799 | + | 0.948089i | ||||
\(325\) | −2.37896 | + | 2.70935i | −0.131961 | + | 0.150288i | ||||
\(326\) | 1.32004 | + | 2.28637i | 0.0731101 | + | 0.126630i | ||||
\(327\) | −24.2629 | + | 1.49622i | −1.34174 | + | 0.0827412i | ||||
\(328\) | 3.66833 | − | 6.35374i | 0.202550 | − | 0.350826i | ||||
\(329\) | −3.28742 | + | 5.69398i | −0.181241 | + | 0.313919i | ||||
\(330\) | 0.657659 | + | 0.992531i | 0.0362030 | + | 0.0546370i | ||||
\(331\) | −20.1502 | + | 11.6337i | −1.10756 | + | 0.639448i | −0.938195 | − | 0.346106i | \(-0.887504\pi\) |
−0.169361 | + | 0.985554i | \(0.554170\pi\) | |||||||
\(332\) | 6.89403i | 0.378359i | ||||||||
\(333\) | 2.11459 | + | 17.0800i | 0.115879 | + | 0.935979i | ||||
\(334\) | 1.68702 | 0.0923096 | ||||||||
\(335\) | −1.94759 | − | 3.37333i | −0.106408 | − | 0.184305i | ||||
\(336\) | 5.66385 | − | 11.3742i | 0.308989 | − | 0.620516i | ||||
\(337\) | 3.89171 | − | 6.74063i | 0.211995 | − | 0.367186i | −0.740344 | − | 0.672228i | \(-0.765337\pi\) |
0.952339 | + | 0.305043i | \(0.0986707\pi\) | |||||||
\(338\) | 0.842914 | − | 2.02798i | 0.0458485 | − | 0.110308i | ||||
\(339\) | 7.85691 | + | 3.91238i | 0.426729 | + | 0.212492i | ||||
\(340\) | 1.21157 | − | 0.699502i | 0.0657067 | − | 0.0379358i | ||||
\(341\) | 20.2153 | 1.09472 | ||||||||
\(342\) | 1.97247 | + | 2.61209i | 0.106659 | + | 0.141246i | ||||
\(343\) | − | 19.7891i | − | 1.06851i | ||||||
\(344\) | −5.05523 | + | 2.91864i | −0.272560 | + | 0.157363i | ||||
\(345\) | 8.01437 | + | 12.0952i | 0.431479 | + | 0.651183i | ||||
\(346\) | 2.35286 | + | 1.35842i | 0.126490 | + | 0.0730293i | ||||
\(347\) | −8.23126 | + | 14.2570i | −0.441877 | + | 0.765354i | −0.997829 | − | 0.0658610i | \(-0.979021\pi\) |
0.555952 | + | 0.831215i | \(0.312354\pi\) | |||||||
\(348\) | 1.48598 | + | 24.0969i | 0.0796571 | + | 1.29173i | ||||
\(349\) | 31.5526 | − | 18.2169i | 1.68897 | − | 0.975127i | 0.733661 | − | 0.679515i | \(-0.237810\pi\) |
0.955308 | − | 0.295611i | \(-0.0955234\pi\) | |||||||
\(350\) | 0.323621 | 0.0172983 | ||||||||
\(351\) | −16.3380 | + | 9.16900i | −0.872057 | + | 0.489405i | ||||
\(352\) | 8.09263 | 0.431339 | ||||||||
\(353\) | 21.2577 | − | 12.2732i | 1.13143 | − | 0.653234i | 0.187139 | − | 0.982333i | \(-0.440078\pi\) |
0.944295 | + | 0.329099i | \(0.106745\pi\) | |||||||
\(354\) | −0.179172 | − | 2.90547i | −0.00952288 | − | 0.154424i | ||||
\(355\) | −2.85012 | + | 4.93655i | −0.151269 | + | 0.262005i | ||||
\(356\) | −17.2324 | − | 9.94915i | −0.913317 | − | 0.527304i | ||||
\(357\) | −1.30053 | − | 1.96275i | −0.0688316 | − | 0.103880i | ||||
\(358\) | −0.977563 | + | 0.564396i | −0.0516658 | + | 0.0298293i | ||||
\(359\) | − | 5.35067i | − | 0.282398i | −0.989981 | − | 0.141199i | \(-0.954904\pi\) | ||
0.989981 | − | 0.141199i | \(-0.0450957\pi\) | |||||||
\(360\) | −0.784594 | + | 1.85357i | −0.0413517 | + | 0.0976915i | ||||
\(361\) | −22.7105 | −1.19529 | ||||||||
\(362\) | 1.78226 | − | 1.02899i | 0.0936736 | − | 0.0540825i | ||||
\(363\) | −8.61651 | − | 4.29063i | −0.452249 | − | 0.225200i | ||||
\(364\) | 12.8967 | − | 4.36908i | 0.675971 | − | 0.229002i | ||||
\(365\) | −2.89656 | + | 5.01698i | −0.151613 | + | 0.262601i | ||||
\(366\) | −0.392957 | + | 0.789143i | −0.0205402 | + | 0.0412491i | ||||
\(367\) | 10.2844 | + | 17.8131i | 0.536841 | + | 0.929836i | 0.999072 | + | 0.0430763i | \(0.0137158\pi\) |
−0.462231 | + | 0.886760i | \(0.652951\pi\) | |||||||
\(368\) | 32.0805 | 1.67231 | ||||||||
\(369\) | −30.2103 | − | 12.7877i | −1.57269 | − | 0.665701i | ||||
\(370\) | 0.969160i | 0.0503842i | ||||||||
\(371\) | −3.05040 | + | 1.76115i | −0.158369 | + | 0.0914342i | ||||
\(372\) | 9.37026 | + | 14.1415i | 0.485825 | + | 0.733201i | ||||
\(373\) | −5.65573 | + | 9.79602i | −0.292843 | + | 0.507219i | −0.974481 | − | 0.224471i | \(-0.927935\pi\) |
0.681638 | + | 0.731690i | \(0.261268\pi\) | |||||||
\(374\) | 0.243906 | − | 0.422457i | 0.0126121 | − | 0.0218447i | ||||
\(375\) | 1.72877 | − | 0.106608i | 0.0892731 | − | 0.00550521i | ||||
\(376\) | −1.15138 | − | 1.99425i | −0.0593780 | − | 0.102846i | ||||
\(377\) | −16.8199 | + | 19.1558i | −0.866268 | + | 0.986576i | ||||
\(378\) | 1.58598 | + | 0.558934i | 0.0815738 | + | 0.0287484i | ||||
\(379\) | 1.06242i | 0.0545727i | 0.999628 | + | 0.0272863i | \(0.00868659\pi\) | ||||
−0.999628 | + | 0.0272863i | \(0.991313\pi\) | |||||||
\(380\) | −6.36621 | − | 11.0266i | −0.326580 | − | 0.565652i | ||||
\(381\) | −0.921789 | − | 14.9478i | −0.0472247 | − | 0.765800i | ||||
\(382\) | −2.41794 | − | 1.39600i | −0.123712 | − | 0.0714254i | ||||
\(383\) | −0.985655 | − | 0.569068i | −0.0503646 | − | 0.0290780i | 0.474606 | − | 0.880198i | \(-0.342590\pi\) |
−0.524971 | + | 0.851120i | \(0.675924\pi\) | |||||||
\(384\) | 4.98903 | + | 7.52937i | 0.254595 | + | 0.384232i | ||||
\(385\) | −6.75053 | + | 3.89742i | −0.344039 | + | 0.198631i | ||||
\(386\) | −2.43023 | −0.123696 | ||||||||
\(387\) | 15.7289 | + | 20.8293i | 0.799544 | + | 1.05882i | ||||
\(388\) | − | 33.0664i | − | 1.67869i | ||||||
\(389\) | 9.07859 | + | 15.7246i | 0.460303 | + | 0.797268i | 0.998976 | − | 0.0452472i | \(-0.0144075\pi\) |
−0.538673 | + | 0.842515i | \(0.681074\pi\) | |||||||
\(390\) | −0.976499 | + | 0.399375i | −0.0494470 | + | 0.0202231i | ||||
\(391\) | 2.97229 | − | 5.14815i | 0.150315 | − | 0.260353i | ||||
\(392\) | 1.93508 | + | 1.11722i | 0.0977362 | + | 0.0564280i | ||||
\(393\) | −7.38032 | − | 3.67506i | −0.372288 | − | 0.185382i | ||||
\(394\) | 2.09231 | + | 3.62399i | 0.105409 | + | 0.182574i | ||||
\(395\) | − | 13.8501i | − | 0.696876i | ||||||
\(396\) | −2.95692 | − | 23.8837i | −0.148591 | − | 1.20020i | ||||
\(397\) | 8.13168i | 0.408118i | 0.978959 | + | 0.204059i | \(0.0654134\pi\) | ||||
−0.978959 | + | 0.204059i | \(0.934587\pi\) | |||||||
\(398\) | −1.39610 | + | 0.806039i | −0.0699802 | + | 0.0404031i | ||||
\(399\) | −17.8631 | + | 11.8362i | −0.894273 | + | 0.592553i | ||||
\(400\) | 1.91479 | − | 3.31651i | 0.0957394 | − | 0.165825i | ||||
\(401\) | 25.7963 | + | 14.8935i | 1.28820 | + | 0.743745i | 0.978334 | − | 0.207033i | \(-0.0663809\pi\) |
0.309871 | + | 0.950779i | \(0.399714\pi\) | |||||||
\(402\) | −0.0701526 | − | 1.13760i | −0.00349889 | − | 0.0567384i | ||||
\(403\) | −3.50525 | + | 17.5662i | −0.174609 | + | 0.875033i | ||||
\(404\) | 13.7714 | 0.685154 | ||||||||
\(405\) | 8.65632 | + | 2.46334i | 0.430136 | + | 0.122404i | ||||
\(406\) | 2.28809 | 0.113556 | ||||||||
\(407\) | −11.6718 | − | 20.2161i | −0.578547 | − | 1.00207i | ||||
\(408\) | 0.823081 | − | 0.0507570i | 0.0407486 | − | 0.00251285i | ||||
\(409\) | −5.57799 | − | 3.22046i | −0.275814 | − | 0.159241i | 0.355713 | − | 0.934595i | \(-0.384238\pi\) |
−0.631527 | + | 0.775354i | \(0.717571\pi\) | |||||||
\(410\) | −1.59985 | − | 0.923673i | −0.0790109 | − | 0.0456170i | ||||
\(411\) | −9.79395 | − | 14.7809i | −0.483100 | − | 0.729088i | ||||
\(412\) | 13.8431 | + | 23.9770i | 0.682002 | + | 1.18126i | ||||
\(413\) | 19.0575 | 0.937758 | ||||||||
\(414\) | 0.521641 | + | 4.21341i | 0.0256372 | + | 0.207078i | ||||
\(415\) | 3.49692 | 0.171657 | ||||||||
\(416\) | −1.40323 | + | 7.03213i | −0.0687990 | + | 0.344778i | ||||
\(417\) | −17.9164 | − | 8.92155i | −0.877370 | − | 0.436890i | ||||
\(418\) | −3.84481 | − | 2.21980i | −0.188056 | − | 0.108574i | ||||
\(419\) | 0.345757 | − | 0.598869i | 0.0168913 | − | 0.0292566i | −0.857456 | − | 0.514557i | \(-0.827956\pi\) |
0.874348 | + | 0.485300i | \(0.161290\pi\) | |||||||
\(420\) | −5.85544 | − | 2.91574i | −0.285716 | − | 0.142274i | ||||
\(421\) | 29.7908 | − | 17.1998i | 1.45192 | − | 0.838265i | 0.453327 | − | 0.891344i | \(-0.350237\pi\) |
0.998590 | + | 0.0530797i | \(0.0169037\pi\) | |||||||
\(422\) | − | 1.52627i | − | 0.0742978i | ||||||
\(423\) | −8.21703 | + | 6.20493i | −0.399526 | + | 0.301694i | ||||
\(424\) | − | 1.23364i | − | 0.0599111i | ||||||
\(425\) | −0.354814 | − | 0.614556i | −0.0172110 | − | 0.0298103i | ||||
\(426\) | −1.39040 | + | 0.921294i | −0.0673653 | + | 0.0446368i | ||||
\(427\) | −4.99818 | − | 2.88570i | −0.241879 | − | 0.139649i | ||||
\(428\) | 7.00952 | − | 12.1408i | 0.338818 | − | 0.586850i | ||||
\(429\) | 15.5594 | − | 20.0909i | 0.751216 | − | 0.969996i | ||||
\(430\) | 0.734904 | + | 1.27289i | 0.0354402 | + | 0.0613842i | ||||
\(431\) | 5.81003i | 0.279859i | 0.990161 | + | 0.139930i | \(0.0446877\pi\) | ||||
−0.990161 | + | 0.139930i | \(0.955312\pi\) | |||||||
\(432\) | 15.1119 | − | 12.9462i | 0.727070 | − | 0.622875i | ||||
\(433\) | −0.137485 | −0.00660711 | −0.00330356 | − | 0.999995i | \(-0.501052\pi\) | ||||
−0.00330356 | + | 0.999995i | \(0.501052\pi\) | |||||||
\(434\) | 1.39236 | − | 0.803879i | 0.0668354 | − | 0.0385874i | ||||
\(435\) | 12.2229 | − | 0.753748i | 0.586041 | − | 0.0361395i | ||||
\(436\) | 23.9621 | + | 13.8345i | 1.14758 | + | 0.662553i | ||||
\(437\) | −46.8536 | − | 27.0510i | −2.24131 | − | 1.29402i | ||||
\(438\) | −1.41306 | + | 0.936304i | −0.0675185 | + | 0.0447383i | ||||
\(439\) | −16.8303 | − | 29.1510i | −0.803267 | − | 1.39130i | −0.917455 | − | 0.397840i | \(-0.869760\pi\) |
0.114188 | − | 0.993459i | \(-0.463573\pi\) | |||||||
\(440\) | − | 2.73006i | − | 0.130150i | ||||||
\(441\) | 3.89459 | − | 9.20078i | 0.185457 | − | 0.438132i | ||||
\(442\) | 0.324804 | + | 0.285195i | 0.0154493 | + | 0.0135654i | ||||
\(443\) | −3.16074 | − | 5.47456i | −0.150171 | − | 0.260104i | 0.781119 | − | 0.624382i | \(-0.214649\pi\) |
−0.931290 | + | 0.364278i | \(0.881316\pi\) | |||||||
\(444\) | 8.73189 | − | 17.5355i | 0.414397 | − | 0.832199i | ||||
\(445\) | −5.04659 | + | 8.74095i | −0.239231 | + | 0.414361i | ||||
\(446\) | −1.25767 | + | 2.17834i | −0.0595522 | + | 0.103147i | ||||
\(447\) | 16.9734 | − | 34.0863i | 0.802815 | − | 1.61223i | ||||
\(448\) | −12.1490 | + | 7.01423i | −0.573987 | + | 0.331391i | ||||
\(449\) | − | 2.50392i | − | 0.118167i | −0.998253 | − | 0.0590836i | \(-0.981182\pi\) | ||
0.998253 | − | 0.0590836i | \(-0.0188178\pi\) | |||||||
\(450\) | 0.466721 | + | 0.197558i | 0.0220015 | + | 0.00931298i | ||||
\(451\) | 44.4958 | 2.09522 | ||||||||
\(452\) | −4.99516 | − | 8.65187i | −0.234953 | − | 0.406950i | ||||
\(453\) | −0.222866 | − | 0.336346i | −0.0104711 | − | 0.0158029i | ||||
\(454\) | −1.38186 | + | 2.39345i | −0.0648537 | + | 0.112330i | ||||
\(455\) | −2.21617 | − | 6.54170i | −0.103895 | − | 0.306680i | ||||
\(456\) | −0.461943 | − | 7.49091i | −0.0216325 | − | 0.350794i | ||||
\(457\) | −14.7320 | + | 8.50550i | −0.689132 | + | 0.397870i | −0.803287 | − | 0.595592i | \(-0.796917\pi\) |
0.114155 | + | 0.993463i | \(0.463584\pi\) | |||||||
\(458\) | −0.392894 | −0.0183588 | ||||||||
\(459\) | −0.677429 | − | 3.62457i | −0.0316197 | − | 0.169181i | ||||
\(460\) | − | 16.5150i | − | 0.770015i | ||||||
\(461\) | 13.4256 | − | 7.75127i | 0.625292 | − | 0.361013i | −0.153634 | − | 0.988128i | \(-0.549098\pi\) |
0.778927 | + | 0.627115i | \(0.215764\pi\) | |||||||
\(462\) | −2.27651 | + | 0.140386i | −0.105913 | + | 0.00653133i | ||||
\(463\) | −31.7351 | − | 18.3223i | −1.47486 | − | 0.851508i | −0.475257 | − | 0.879847i | \(-0.657645\pi\) |
−0.999598 | + | 0.0283393i | \(0.990978\pi\) | |||||||
\(464\) | 13.5381 | − | 23.4486i | 0.628490 | − | 1.08858i | ||||
\(465\) | 7.17310 | − | 4.75295i | 0.332644 | − | 0.220413i | ||||
\(466\) | 1.24108 | − | 0.716539i | 0.0574920 | − | 0.0331930i | ||||
\(467\) | 10.1586 | 0.470084 | 0.235042 | − | 0.971985i | \(-0.424477\pi\) | ||||
0.235042 | + | 0.971985i | \(0.424477\pi\) | |||||||
\(468\) | 21.2666 | + | 1.57191i | 0.983048 | + | 0.0726616i | ||||
\(469\) | 7.46173 | 0.344551 | ||||||||
\(470\) | −0.502146 | + | 0.289914i | −0.0231623 | + | 0.0133727i | ||||
\(471\) | 31.9029 | + | 15.8862i | 1.47001 | + | 0.731996i | ||||
\(472\) | −3.33734 | + | 5.78044i | −0.153613 | + | 0.266066i | ||||
\(473\) | −30.6593 | − | 17.7011i | −1.40971 | − | 0.813899i | ||||
\(474\) | 1.80646 | − | 3.62777i | 0.0829737 | − | 0.166629i | ||||
\(475\) | −5.59311 | + | 3.22918i | −0.256630 | + | 0.148165i | ||||
\(476\) | 2.67997i | 0.122836i | ||||||||
\(477\) | −5.47435 | + | 0.677752i | −0.250653 | + | 0.0310321i | ||||
\(478\) | −1.52782 | −0.0698808 | ||||||||
\(479\) | 5.55588 | − | 3.20769i | 0.253855 | − | 0.146563i | −0.367673 | − | 0.929955i | \(-0.619846\pi\) |
0.621528 | + | 0.783392i | \(0.286512\pi\) | |||||||
\(480\) | 2.87155 | − | 1.90271i | 0.131068 | − | 0.0868466i | ||||
\(481\) | 19.5907 | − | 6.63684i | 0.893258 | − | 0.302614i | ||||
\(482\) | −0.713571 | + | 1.23594i | −0.0325023 | + | 0.0562956i | ||||
\(483\) | −27.7420 | + | 1.71077i | −1.26230 | + | 0.0778426i | ||||
\(484\) | 5.47809 | + | 9.48832i | 0.249004 | + | 0.431287i | ||||
\(485\) | −16.7725 | −0.761602 | ||||||||
\(486\) | 1.94606 | + | 1.77426i | 0.0882752 | + | 0.0804822i | ||||
\(487\) | 20.7706i | 0.941204i | 0.882346 | + | 0.470602i | \(0.155963\pi\) | ||||
−0.882346 | + | 0.470602i | \(0.844037\pi\) | |||||||
\(488\) | 1.75056 | − | 1.01068i | 0.0792439 | − | 0.0457515i | ||||
\(489\) | −27.0164 | + | 1.66602i | −1.22172 | + | 0.0753401i | ||||
\(490\) | 0.281312 | − | 0.487246i | 0.0127084 | − | 0.0220115i | ||||
\(491\) | 1.95213 | − | 3.38118i | 0.0880982 | − | 0.152591i | −0.818609 | − | 0.574351i | \(-0.805254\pi\) |
0.906707 | + | 0.421761i | \(0.138588\pi\) | |||||||
\(492\) | 20.6248 | + | 31.1267i | 0.929840 | + | 1.40330i | ||||
\(493\) | −2.50863 | − | 4.34508i | −0.112983 | − | 0.195693i | ||||
\(494\) | 2.59558 | − | 2.95606i | 0.116781 | − | 0.132999i | ||||
\(495\) | −12.1147 | + | 1.49987i | −0.544517 | + | 0.0674139i | ||||
\(496\) | − | 19.0254i | − | 0.854267i | ||||||
\(497\) | −5.45977 | − | 9.45660i | −0.244904 | − | 0.424186i | ||||
\(498\) | 0.915948 | + | 0.456100i | 0.0410446 | + | 0.0204383i | ||||
\(499\) | −2.91052 | − | 1.68039i | −0.130293 | − | 0.0752246i | 0.433437 | − | 0.901184i | \(-0.357301\pi\) |
−0.563730 | + | 0.825959i | \(0.690634\pi\) | |||||||
\(500\) | −1.70733 | − | 0.985730i | −0.0763543 | − | 0.0440832i | ||||
\(501\) | −7.70983 | + | 15.4830i | −0.344450 | + | 0.691730i | ||||
\(502\) | −0.756521 | + | 0.436778i | −0.0337652 | + | 0.0194943i | ||||
\(503\) | −18.6413 | −0.831173 | −0.415586 | − | 0.909554i | \(-0.636424\pi\) | ||||
−0.415586 | + | 0.909554i | \(0.636424\pi\) | |||||||
\(504\) | −2.32354 | − | 3.07700i | −0.103499 | − | 0.137060i | ||||
\(505\) | − | 6.98539i | − | 0.310846i | ||||||
\(506\) | −2.87926 | − | 4.98703i | −0.127999 | − | 0.221700i | ||||
\(507\) | 14.7601 | + | 17.0041i | 0.655519 | + | 0.755179i | ||||
\(508\) | −8.52314 | + | 14.7625i | −0.378153 | + | 0.654980i | ||||
\(509\) | 0.552125 | + | 0.318770i | 0.0244725 | + | 0.0141292i | 0.512186 | − | 0.858874i | \(-0.328836\pi\) |
−0.487714 | + | 0.873004i | \(0.662169\pi\) | |||||||
\(510\) | −0.0127804 | − | 0.207249i | −0.000565928 | − | 0.00917714i | ||||
\(511\) | −5.54872 | − | 9.61067i | −0.245461 | − | 0.425151i | ||||
\(512\) | − | 12.7550i | − | 0.563699i | ||||||
\(513\) | −32.9875 | + | 6.16532i | −1.45643 | + | 0.272206i | ||||
\(514\) | 1.38437i | 0.0610617i | ||||||||
\(515\) | 12.1620 | − | 7.02176i | 0.535924 | − | 0.309416i | ||||
\(516\) | −1.82858 | − | 29.6524i | −0.0804985 | − | 1.30537i | ||||
\(517\) | 6.98297 | − | 12.0949i | 0.307111 | − | 0.531931i | ||||
\(518\) | −1.60782 | − | 0.928275i | −0.0706436 | − | 0.0407861i | ||||
\(519\) | −23.2200 | + | 15.3858i | −1.01925 | + | 0.675361i | ||||
\(520\) | 2.37229 | + | 0.473381i | 0.104032 | + | 0.0207591i | ||||
\(521\) | −11.6561 | −0.510662 | −0.255331 | − | 0.966854i | \(-0.582184\pi\) | ||||
−0.255331 | + | 0.966854i | \(0.582184\pi\) | |||||||
\(522\) | 3.29985 | + | 1.39679i | 0.144431 | + | 0.0611359i | ||||
\(523\) | −21.6071 | −0.944814 | −0.472407 | − | 0.881381i | \(-0.656615\pi\) | ||||
−0.472407 | + | 0.881381i | \(0.656615\pi\) | |||||||
\(524\) | 4.69216 | + | 8.12706i | 0.204978 | + | 0.355032i | ||||
\(525\) | −1.47898 | + | 2.97011i | −0.0645478 | + | 0.129626i | ||||
\(526\) | −2.01679 | − | 1.16439i | −0.0879362 | − | 0.0507700i | ||||
\(527\) | −3.05313 | − | 1.76273i | −0.132996 | − | 0.0767855i | ||||
\(528\) | −12.0309 | + | 24.1606i | −0.523576 | + | 1.05145i | ||||
\(529\) | −23.5873 | − | 40.8544i | −1.02553 | − | 1.77628i | ||||
\(530\) | −0.310627 | −0.0134928 | ||||||||
\(531\) | 27.4845 | + | 11.6339i | 1.19272 | + | 0.504867i | ||||
\(532\) | 24.3906 | 1.05747 | ||||||||
\(533\) | −7.71539 | + | 38.6648i | −0.334191 | + | 1.67476i | ||||
\(534\) | −2.46193 | + | 1.63130i | −0.106538 | + | 0.0705931i | ||||
\(535\) | −6.15830 | − | 3.55550i | −0.266246 | − | 0.153717i | ||||
\(536\) | −1.30669 | + | 2.26326i | −0.0564406 | + | 0.0977580i | ||||
\(537\) | −0.712326 | − | 11.5512i | −0.0307391 | − | 0.498469i | ||||
\(538\) | −2.44214 | + | 1.40997i | −0.105288 | + | 0.0607881i | ||||
\(539\) | 13.5515i | 0.583705i | ||||||||
\(540\) | −6.66469 | − | 7.77957i | −0.286802 | − | 0.334779i | ||||
\(541\) | 32.3894i | 1.39253i | 0.717785 | + | 0.696265i | \(0.245156\pi\) | ||||
−0.717785 | + | 0.696265i | \(0.754844\pi\) | |||||||
\(542\) | −0.114123 | − | 0.197666i | −0.00490199 | − | 0.00849050i | ||||
\(543\) | 1.29869 | + | 21.0597i | 0.0557321 | + | 0.903758i | ||||
\(544\) | −1.22224 | − | 0.705659i | −0.0524030 | − | 0.0302549i | ||||
\(545\) | 7.01740 | − | 12.1545i | 0.300592 | − | 0.520641i | ||||
\(546\) | 0.272749 | − | 2.00252i | 0.0116726 | − | 0.0857001i | ||||
\(547\) | −1.61348 | − | 2.79463i | −0.0689875 | − | 0.119490i | 0.829468 | − | 0.558554i | \(-0.188644\pi\) |
−0.898456 | + | 0.439064i | \(0.855310\pi\) | |||||||
\(548\) | 20.1821i | 0.862137i | ||||||||
\(549\) | −5.44669 | − | 7.21290i | −0.232459 | − | 0.307839i | ||||
\(550\) | −0.687419 | −0.0293116 | ||||||||
\(551\) | −39.5448 | + | 22.8312i | −1.68467 | + | 0.972643i | ||||
\(552\) | 4.33926 | − | 8.71417i | 0.184691 | − | 0.370900i | ||||
\(553\) | 22.9771 | + | 13.2659i | 0.977087 | + | 0.564122i | ||||
\(554\) | −1.16633 | − | 0.673381i | −0.0495526 | − | 0.0286092i | ||||
\(555\) | −8.89469 | − | 4.42915i | −0.377559 | − | 0.188007i | ||||
\(556\) | 11.3906 | + | 19.7292i | 0.483071 | + | 0.836703i | ||||
\(557\) | − | 10.5473i | − | 0.446904i | −0.974715 | − | 0.223452i | \(-0.928267\pi\) | ||
0.974715 | − | 0.223452i | \(-0.0717325\pi\) | |||||||
\(558\) | 2.49878 | − | 0.309361i | 0.105782 | − | 0.0130963i | ||||
\(559\) | 20.6977 | − | 23.5722i | 0.875418 | − | 0.996997i | ||||
\(560\) | 3.66802 | + | 6.35320i | 0.155002 | + | 0.268472i | ||||
\(561\) | 2.76253 | + | 4.16917i | 0.116634 | + | 0.176022i | ||||
\(562\) | 2.05399 | − | 3.55762i | 0.0866424 | − | 0.150069i | ||||
\(563\) | −5.75539 | + | 9.96864i | −0.242561 | + | 0.420128i | −0.961443 | − | 0.275004i | \(-0.911321\pi\) |
0.718882 | + | 0.695132i | \(0.244654\pi\) | |||||||
\(564\) | 11.6977 | − | 0.721360i | 0.492560 | − | 0.0303747i | ||||
\(565\) | −4.38856 | + | 2.53374i | −0.184628 | + | 0.106595i | ||||
\(566\) | − | 2.59778i | − | 0.109193i | ||||||
\(567\) | −12.3778 | + | 12.0013i | −0.519818 | + | 0.504006i | ||||
\(568\) | 3.82445 | 0.160470 | ||||||||
\(569\) | −11.4118 | − | 19.7658i | −0.478406 | − | 0.828624i | 0.521287 | − | 0.853381i | \(-0.325452\pi\) |
−0.999693 | + | 0.0247571i | \(0.992119\pi\) | |||||||
\(570\) | −1.88619 | + | 0.116316i | −0.0790036 | + | 0.00487192i | ||||
\(571\) | −3.66812 | + | 6.35337i | −0.153506 | + | 0.265880i | −0.932514 | − | 0.361134i | \(-0.882390\pi\) |
0.779008 | + | 0.627014i | \(0.215723\pi\) | |||||||
\(572\) | −27.3945 | + | 9.28057i | −1.14542 | + | 0.388040i | ||||
\(573\) | 23.8623 | − | 15.8113i | 0.996861 | − | 0.660529i | ||||
\(574\) | 3.06472 | − | 1.76941i | 0.127919 | − | 0.0738539i | ||||
\(575\) | −8.37703 | −0.349346 | ||||||||
\(576\) | −21.8030 | + | 2.69933i | −0.908460 | + | 0.112472i | ||||
\(577\) | − | 10.2351i | − | 0.426092i | −0.977042 | − | 0.213046i | \(-0.931662\pi\) | ||
0.977042 | − | 0.213046i | \(-0.0683385\pi\) | |||||||
\(578\) | 2.41349 | − | 1.39343i | 0.100388 | − | 0.0579591i | ||||
\(579\) | 11.1064 | − | 22.3040i | 0.461566 | − | 0.926924i | ||||
\(580\) | −12.0713 | − | 6.96939i | −0.501235 | − | 0.289388i | ||||
\(581\) | −3.34940 | + | 5.80132i | −0.138956 | + | 0.240679i | ||||
\(582\) | −4.39324 | − | 2.18763i | −0.182106 | − | 0.0906803i | ||||
\(583\) | 6.47949 | − | 3.74094i | 0.268353 | − | 0.154934i | ||||
\(584\) | 3.88676 | 0.160835 | ||||||||
\(585\) | 0.797333 | − | 10.7872i | 0.0329657 | − | 0.445997i | ||||
\(586\) | −3.35959 | −0.138784 | ||||||||
\(587\) | 32.3746 | − | 18.6915i | 1.33624 | − | 0.771481i | 0.349996 | − | 0.936751i | \(-0.386183\pi\) |
0.986248 | + | 0.165270i | \(0.0528496\pi\) | |||||||
\(588\) | −9.47988 | + | 6.28145i | −0.390944 | + | 0.259043i | ||||
\(589\) | −16.0427 | + | 27.7867i | −0.661027 | + | 1.14493i | ||||
\(590\) | 1.45549 | + | 0.840330i | 0.0599218 | + | 0.0345959i | ||||
\(591\) | −42.8221 | + | 2.64071i | −1.76147 | + | 0.108624i | ||||
\(592\) | −19.0262 | + | 10.9848i | −0.781971 | + | 0.451471i | ||||
\(593\) | 8.06905i | 0.331356i | 0.986180 | + | 0.165678i | \(0.0529812\pi\) | ||||
−0.986180 | + | 0.165678i | \(0.947019\pi\) | |||||||
\(594\) | −3.36884 | − | 1.18726i | −0.138225 | − | 0.0487138i | ||||
\(595\) | 1.35938 | 0.0557293 | ||||||||
\(596\) | −37.5351 | + | 21.6709i | −1.53750 | + | 0.887676i | ||||
\(597\) | −1.01730 | − | 16.4967i | −0.0416354 | − | 0.675165i | ||||
\(598\) | 4.83275 | − | 1.63722i | 0.197626 | − | 0.0669508i | ||||
\(599\) | 19.9770 | − | 34.6011i | 0.816237 | − | 1.41376i | −0.0921994 | − | 0.995741i | \(-0.529390\pi\) |
0.908436 | − | 0.418023i | \(-0.137277\pi\) | |||||||
\(600\) | −0.641882 | − | 0.968720i | −0.0262047 | − | 0.0395478i | ||||
\(601\) | −9.30397 | − | 16.1150i | −0.379517 | − | 0.657343i | 0.611475 | − | 0.791264i | \(-0.290576\pi\) |
−0.990992 | + | 0.133921i | \(0.957243\pi\) | |||||||
\(602\) | −2.81560 | −0.114755 | ||||||||
\(603\) | 10.7612 | + | 4.55510i | 0.438230 | + | 0.185498i | ||||
\(604\) | 0.459253i | 0.0186867i | ||||||||
\(605\) | 4.81284 | − | 2.77869i | 0.195670 | − | 0.112970i | ||||
\(606\) | 0.911101 | − | 1.82969i | 0.0370109 | − | 0.0743260i | ||||
\(607\) | 1.43661 | − | 2.48828i | 0.0583102 | − | 0.100996i | −0.835397 | − | 0.549647i | \(-0.814762\pi\) |
0.893707 | + | 0.448651i | \(0.148095\pi\) | |||||||
\(608\) | −6.42224 | + | 11.1236i | −0.260456 | + | 0.451124i | ||||
\(609\) | −10.4568 | + | 20.9995i | −0.423730 | + | 0.850942i | ||||
\(610\) | −0.254487 | − | 0.440784i | −0.0103039 | − | 0.0178468i | ||||
\(611\) | 9.29906 | + | 8.16508i | 0.376200 | + | 0.330324i | ||||
\(612\) | −1.63602 | + | 3.86501i | −0.0661321 | + | 0.156234i | ||||
\(613\) | 35.4684i | 1.43256i | 0.697815 | + | 0.716278i | \(0.254156\pi\) | ||||
−0.697815 | + | 0.716278i | \(0.745844\pi\) | |||||||
\(614\) | 0.172791 | + | 0.299283i | 0.00697328 | + | 0.0120781i | ||||
\(615\) | 15.7887 | − | 10.4617i | 0.636661 | − | 0.421857i | ||||
\(616\) | 4.52912 | + | 2.61489i | 0.182483 | + | 0.105357i | ||||
\(617\) | 8.29254 | + | 4.78770i | 0.333845 | + | 0.192746i | 0.657547 | − | 0.753414i | \(-0.271594\pi\) |
−0.323702 | + | 0.946159i | \(0.604927\pi\) | |||||||
\(618\) | 4.10145 | − | 0.252925i | 0.164985 | − | 0.0101741i | ||||
\(619\) | 31.7560 | − | 18.3343i | 1.27638 | − | 0.736920i | 0.300201 | − | 0.953876i | \(-0.402946\pi\) |
0.976181 | + | 0.216956i | \(0.0696129\pi\) | |||||||
\(620\) | −9.79427 | −0.393347 | ||||||||
\(621\) | −41.0535 | − | 14.4682i | −1.64742 | − | 0.580588i | ||||
\(622\) | 3.82815i | 0.153495i | ||||||||
\(623\) | −9.66739 | − | 16.7444i | −0.387316 | − | 0.670851i | ||||
\(624\) | −18.9083 | − | 14.6436i | −0.756939 | − | 0.586214i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −1.13537 | − | 0.655504i | −0.0453783 | − | 0.0261992i | ||||
\(627\) | 37.9438 | − | 25.1419i | 1.51533 | − | 1.00407i | ||||
\(628\) | −20.2828 | − | 35.1308i | −0.809370 | − | 1.40187i | ||||
\(629\) | 4.07100i | 0.162321i | ||||||||
\(630\) | −0.774778 | + | 0.585059i | −0.0308679 | + | 0.0233093i | ||||
\(631\) | 3.30174i | 0.131440i | 0.997838 | + | 0.0657201i | \(0.0209345\pi\) | ||||
−0.997838 | + | 0.0657201i | \(0.979066\pi\) | |||||||
\(632\) | −8.04749 | + | 4.64622i | −0.320112 | + | 0.184817i | ||||
\(633\) | 14.0077 | + | 6.97520i | 0.556757 | + | 0.277239i | ||||
\(634\) | −0.407283 | + | 0.705435i | −0.0161753 | + | 0.0280164i | ||||
\(635\) | 7.48811 | + | 4.32326i | 0.297157 | + | 0.171563i | ||||
\(636\) | 5.62035 | + | 2.79868i | 0.222861 | + | 0.110975i | ||||
\(637\) | −11.7757 | − | 2.34978i | −0.466568 | − | 0.0931017i | ||||
\(638\) | −4.86024 | −0.192419 | ||||||||
\(639\) | −2.10111 | − | 16.9711i | −0.0831187 | − | 0.671368i | ||||
\(640\) | −5.21478 | −0.206132 | ||||||||
\(641\) | 23.0575 | + | 39.9368i | 0.910718 | + | 1.57741i | 0.813052 | + | 0.582191i | \(0.197804\pi\) |
0.0976661 | + | 0.995219i | \(0.468862\pi\) | |||||||
\(642\) | −1.14930 | − | 1.73452i | −0.0453594 | − | 0.0684559i | ||||
\(643\) | 15.7548 | + | 9.09606i | 0.621310 | + | 0.358713i | 0.777379 | − | 0.629033i | \(-0.216549\pi\) |
−0.156069 | + | 0.987746i | \(0.549882\pi\) | |||||||
\(644\) | 27.3981 | + | 15.8183i | 1.07963 | + | 0.623328i | ||||
\(645\) | −15.0408 | + | 0.927523i | −0.592232 | + | 0.0365212i | ||||
\(646\) | 0.387123 | + | 0.670517i | 0.0152311 | + | 0.0263811i | ||||
\(647\) | 43.5855 | 1.71352 | 0.856761 | − | 0.515714i | \(-0.172473\pi\) | ||||
0.856761 | + | 0.515714i | \(0.172473\pi\) | |||||||
\(648\) | −1.47258 | − | 5.85603i | −0.0578485 | − | 0.230047i | ||||
\(649\) | −40.4809 | −1.58902 | ||||||||
\(650\) | 0.119196 | − | 0.597335i | 0.00467524 | − | 0.0234294i | ||||
\(651\) | 1.01458 | + | 16.4525i | 0.0397644 | + | 0.644824i | ||||
\(652\) | 26.6815 | + | 15.4045i | 1.04493 | + | 0.603289i | ||||
\(653\) | 11.5654 | − | 20.0318i | 0.452587 | − | 0.783904i | −0.545958 | − | 0.837812i | \(-0.683834\pi\) |
0.998546 | + | 0.0539078i | \(0.0171677\pi\) | |||||||
\(654\) | 3.42337 | − | 2.26835i | 0.133864 | − | 0.0886997i | ||||
\(655\) | 4.12236 | − | 2.38004i | 0.161074 | − | 0.0929960i | ||||
\(656\) | − | 41.8768i | − | 1.63501i | ||||||
\(657\) | −2.13535 | − | 17.2477i | −0.0833078 | − | 0.672895i | ||||
\(658\) | − | 1.11074i | − | 0.0433010i | ||||||
\(659\) | −7.11951 | − | 12.3314i | −0.277337 | − | 0.480361i | 0.693385 | − | 0.720567i | \(-0.256118\pi\) |
−0.970722 | + | 0.240206i | \(0.922785\pi\) | |||||||
\(660\) | 12.4378 | + | 6.19347i | 0.484142 | + | 0.241080i | ||||
\(661\) | −35.9030 | − | 20.7286i | −1.39647 | − | 0.806250i | −0.402446 | − | 0.915444i | \(-0.631840\pi\) |
−0.994021 | + | 0.109194i | \(0.965173\pi\) | |||||||
\(662\) | 1.96537 | − | 3.40412i | 0.0763863 | − | 0.132305i | ||||
\(663\) | −4.10183 | + | 1.67759i | −0.159302 | + | 0.0651523i | ||||
\(664\) | −1.17309 | − | 2.03185i | −0.0455247 | − | 0.0788510i | ||||
\(665\) | − | 12.3718i | − | 0.479759i | ||||||
\(666\) | −1.75210 | − | 2.32026i | −0.0678924 | − | 0.0899082i | ||||
\(667\) | −59.2279 | −2.29331 | ||||||||
\(668\) | 17.0496 | − | 9.84358i | 0.659668 | − | 0.380859i | ||||
\(669\) | −14.2446 | − | 21.4977i | −0.550727 | − | 0.831150i | ||||
\(670\) | 0.569881 | + | 0.329021i | 0.0220164 | + | 0.0127112i | ||||
\(671\) | 10.6169 | + | 6.12965i | 0.409859 | + | 0.236632i | ||||
\(672\) | 0.406158 | + | 6.58630i | 0.0156679 | + | 0.254072i | ||||
\(673\) | 11.7253 | + | 20.3088i | 0.451976 | + | 0.782846i | 0.998509 | − | 0.0545919i | \(-0.0173858\pi\) |
−0.546532 | + | 0.837438i | \(0.684052\pi\) | |||||||
\(674\) | 1.31491i | 0.0506484i | ||||||||
\(675\) | −3.94609 | + | 3.38058i | −0.151885 | + | 0.130119i | ||||
\(676\) | −3.31430 | − | 25.4138i | −0.127473 | − | 0.977453i | ||||
\(677\) | −0.562558 | − | 0.974380i | −0.0216209 | − | 0.0374484i | 0.855013 | − | 0.518607i | \(-0.173549\pi\) |
−0.876633 | + | 0.481159i | \(0.840216\pi\) | |||||||
\(678\) | −1.47997 | + | 0.0912655i | −0.0568379 | + | 0.00350503i | ||||
\(679\) | 16.0650 | − | 27.8254i | 0.616517 | − | 1.06784i | ||||
\(680\) | −0.238054 | + | 0.412322i | −0.00912897 | + | 0.0158118i | ||||
\(681\) | −15.6512 | − | 23.6206i | −0.599755 | − | 0.905142i | ||||
\(682\) | −2.95758 | + | 1.70756i | −0.113251 | + | 0.0653857i | ||||
\(683\) | − | 12.0170i | − | 0.459819i | −0.973212 | − | 0.229910i | \(-0.926157\pi\) | ||
0.973212 | − | 0.229910i | \(-0.0738430\pi\) | |||||||
\(684\) | 35.1757 | + | 14.8895i | 1.34498 | + | 0.569314i | ||||
\(685\) | 10.2371 | 0.391141 | ||||||||
\(686\) | 1.67156 | + | 2.89523i | 0.0638205 | + | 0.110540i | ||||
\(687\) | 1.79556 | − | 3.60588i | 0.0685050 | − | 0.137573i | ||||
\(688\) | −16.6593 | + | 28.8547i | −0.635128 | + | 1.10007i | ||||
\(689\) | 2.12719 | + | 6.27905i | 0.0810393 | + | 0.239213i | ||||
\(690\) | −2.19420 | − | 1.09261i | −0.0835317 | − | 0.0415950i | ||||
\(691\) | −31.5057 | + | 18.1898i | −1.19853 | + | 0.691973i | −0.960228 | − | 0.279218i | \(-0.909925\pi\) |
−0.238304 | + | 0.971191i | \(0.576591\pi\) | |||||||
\(692\) | 31.7050 | 1.20524 | ||||||||
\(693\) | 9.11542 | − | 21.5347i | 0.346266 | − | 0.818037i | ||||
\(694\) | − | 2.78113i | − | 0.105570i | ||||||
\(695\) | 10.0074 | − | 5.77777i | 0.379602 | − | 0.219163i | ||||
\(696\) | −4.53829 | − | 6.84912i | −0.172023 | − | 0.259615i | ||||
\(697\) | −6.72023 | − | 3.87993i | −0.254547 | − | 0.146963i | ||||
\(698\) | −3.07751 | + | 5.33040i | −0.116485 | + | 0.201759i | ||||
\(699\) | 0.904345 | + | 14.6650i | 0.0342055 | + | 0.554680i | ||||
\(700\) | 3.27062 | − | 1.88829i | 0.123618 | − | 0.0713708i | ||||
\(701\) | 14.7142 | 0.555748 | 0.277874 | − | 0.960618i | \(-0.410370\pi\) | ||||
0.277874 | + | 0.960618i | \(0.410370\pi\) | |||||||
\(702\) | 1.61582 | − | 2.72151i | 0.0609851 | − | 0.102717i | ||||
\(703\) | 37.0504 | 1.39738 | ||||||||
\(704\) | 25.8063 | − | 14.8993i | 0.972611 | − | 0.561537i | ||||
\(705\) | −0.365901 | − | 5.93350i | −0.0137806 | − | 0.223468i | ||||
\(706\) | −2.07339 | + | 3.59122i | −0.0780332 | + | 0.135157i | ||||
\(707\) | 11.5887 | + | 6.69071i | 0.435836 | + | 0.251630i | ||||
\(708\) | −18.7639 | − | 28.3182i | −0.705189 | − | 1.06426i | ||||
\(709\) | −8.92475 | + | 5.15271i | −0.335176 | + | 0.193514i | −0.658137 | − | 0.752898i | \(-0.728655\pi\) |
0.322961 | + | 0.946412i | \(0.395322\pi\) | |||||||
\(710\) | − | 0.962983i | − | 0.0361401i | ||||||
\(711\) | 25.0390 | + | 33.1585i | 0.939036 | + | 1.24354i | ||||
\(712\) | 6.77179 | 0.253784 | ||||||||
\(713\) | −36.0416 | + | 20.8086i | −1.34977 | + | 0.779290i | ||||
\(714\) | 0.356064 | + | 0.177304i | 0.0133254 | + | 0.00663542i | ||||
\(715\) | 4.70746 | + | 13.8955i | 0.176049 | + | 0.519664i | ||||
\(716\) | −6.58638 | + | 11.4079i | −0.246145 | + | 0.426335i | ||||
\(717\) | 6.98227 | − | 14.0219i | 0.260757 | − | 0.523657i | ||||
\(718\) | 0.451964 | + | 0.782824i | 0.0168671 | + | 0.0292147i | ||||
\(719\) | 14.8608 | 0.554214 | 0.277107 | − | 0.960839i | \(-0.410624\pi\) | ||||
0.277107 | + | 0.960839i | \(0.410624\pi\) | |||||||
\(720\) | 1.41158 | + | 11.4017i | 0.0526067 | + | 0.424915i | ||||
\(721\) | 26.9022i | 1.00189i | ||||||||
\(722\) | 3.32264 | − | 1.91833i | 0.123656 | − | 0.0713927i | ||||
\(723\) | −8.08205 | − | 12.1973i | −0.300575 | − | 0.453623i | ||||
\(724\) | 12.0081 | − | 20.7986i | 0.446277 | − | 0.772974i | ||||
\(725\) | −3.53514 | + | 6.12304i | −0.131292 | + | 0.227404i | ||||
\(726\) | 1.62305 | − | 0.100089i | 0.0602371 | − | 0.00371465i | ||||
\(727\) | 10.5033 | + | 18.1923i | 0.389547 | + | 0.674715i | 0.992389 | − | 0.123146i | \(-0.0392984\pi\) |
−0.602842 | + | 0.797861i | \(0.705965\pi\) | |||||||
\(728\) | −3.05755 | + | 3.48218i | −0.113320 | + | 0.129058i | ||||
\(729\) | −25.1774 | + | 9.75190i | −0.932496 | + | 0.361181i | ||||
\(730\) | − | 0.978672i | − | 0.0362223i | ||||||
\(731\) | 3.08699 | + | 5.34683i | 0.114177 | + | 0.197760i | ||||
\(732\) | 0.633210 | + | 10.2682i | 0.0234041 | + | 0.379523i | ||||
\(733\) | −27.4355 | − | 15.8399i | −1.01335 | − | 0.585059i | −0.101180 | − | 0.994868i | \(-0.532262\pi\) |
−0.912171 | + | 0.409809i | \(0.865595\pi\) | |||||||
\(734\) | −3.00929 | − | 1.73742i | −0.111075 | − | 0.0641292i | ||||
\(735\) | 3.18619 | + | 4.80856i | 0.117524 | + | 0.177366i | ||||
\(736\) | −14.4283 | + | 8.33017i | −0.531833 | + | 0.307054i | ||||
\(737\) | −15.8498 | −0.583835 | ||||||||
\(738\) | 5.50005 | − | 0.680933i | 0.202460 | − | 0.0250655i | ||||
\(739\) | − | 1.83321i | − | 0.0674357i | −0.999431 | − | 0.0337178i | \(-0.989265\pi\) | ||
0.999431 | − | 0.0337178i | \(-0.0107348\pi\) | |||||||
\(740\) | 5.65494 | + | 9.79465i | 0.207880 | + | 0.360058i | ||||
\(741\) | 15.2679 | + | 37.3310i | 0.560879 | + | 1.37139i | ||||
\(742\) | 0.297523 | − | 0.515326i | 0.0109224 | − | 0.0189182i | ||||
\(743\) | 3.03436 | + | 1.75189i | 0.111320 | + | 0.0642705i | 0.554626 | − | 0.832100i | \(-0.312861\pi\) |
−0.443306 | + | 0.896370i | \(0.646195\pi\) | |||||||
\(744\) | −5.16797 | − | 2.57341i | −0.189467 | − | 0.0943459i | ||||
\(745\) | 10.9923 | + | 19.0393i | 0.402727 | + | 0.697544i | ||||
\(746\) | − | 1.91093i | − | 0.0699640i | ||||||
\(747\) | −8.37193 | + | 6.32191i | −0.306313 | + | 0.231306i | ||||
\(748\) | − | 5.69265i | − | 0.208144i | ||||||
\(749\) | 11.7970 | − | 6.81101i | 0.431053 | − | 0.248869i | ||||
\(750\) | −0.243920 | + | 0.161624i | −0.00890671 | + | 0.00590166i | ||||
\(751\) | 17.3289 | − | 30.0145i | 0.632341 | − | 1.09525i | −0.354731 | − | 0.934968i | \(-0.615428\pi\) |
0.987072 | − | 0.160278i | \(-0.0512391\pi\) | |||||||
\(752\) | −11.3830 | − | 6.57196i | −0.415094 | − | 0.239655i | ||||
\(753\) | −0.551258 | − | 8.93926i | −0.0200890 | − | 0.325765i | ||||
\(754\) | 0.842746 | − | 4.22333i | 0.0306910 | − | 0.153805i | ||||
\(755\) | 0.232951 | 0.00847794 | ||||||||
\(756\) | 19.2897 | − | 3.60522i | 0.701560 | − | 0.131121i | ||||
\(757\) | 3.05994 | 0.111216 | 0.0556078 | − | 0.998453i | \(-0.482290\pi\) | ||||
0.0556078 | + | 0.998453i | \(0.482290\pi\) | |||||||
\(758\) | −0.0897409 | − | 0.155436i | −0.00325954 | − | 0.00564568i | ||||
\(759\) | 58.9281 | − | 3.63392i | 2.13895 | − | 0.131903i | ||||
\(760\) | 3.75257 | + | 2.16655i | 0.136120 | + | 0.0785890i | ||||
\(761\) | 24.7251 | + | 14.2750i | 0.896283 | + | 0.517469i | 0.875993 | − | 0.482325i | \(-0.160207\pi\) |
0.0202909 | + | 0.999794i | \(0.493541\pi\) | |||||||
\(762\) | 1.39748 | + | 2.10906i | 0.0506255 | + | 0.0764033i | ||||
\(763\) | 13.4427 | + | 23.2835i | 0.486659 | + | 0.842919i | ||||
\(764\) | −32.5820 | −1.17877 | ||||||||
\(765\) | 1.96048 | + | 0.829851i | 0.0708814 | + | 0.0300033i | ||||
\(766\) | 0.192274 | 0.00694713 | ||||||||
\(767\) | 7.01924 | − | 35.1761i | 0.253450 | − | 1.27014i | ||||
\(768\) | 21.3426 | + | 10.6277i | 0.770136 | + | 0.383493i | ||||
\(769\) | 5.78804 | + | 3.34173i | 0.208722 | + | 0.120506i | 0.600717 | − | 0.799461i | \(-0.294882\pi\) |
−0.391995 | + | 0.919967i | \(0.628215\pi\) | |||||||
\(770\) | 0.658419 | − | 1.14042i | 0.0237278 | − | 0.0410977i | ||||
\(771\) | −12.7053 | − | 6.32667i | −0.457571 | − | 0.227850i | ||||
\(772\) | −24.5607 | + | 14.1801i | −0.883960 | + | 0.510355i | ||||
\(773\) | − | 7.34991i | − | 0.264358i | −0.991226 | − | 0.132179i | \(-0.957803\pi\) | ||
0.991226 | − | 0.132179i | \(-0.0421973\pi\) | |||||||
\(774\) | −4.06062 | − | 1.71882i | −0.145956 | − | 0.0617816i | ||||
\(775\) | 4.96803i | 0.178457i | ||||||||
\(776\) | 5.62658 | + | 9.74552i | 0.201982 | + | 0.349844i | ||||
\(777\) | 15.8673 | − | 10.5138i | 0.569238 | − | 0.377182i | ||||
\(778\) | −2.65647 | − | 1.53371i | −0.0952389 | − | 0.0549862i | ||||
\(779\) | −35.3115 | + | 61.1612i | −1.26516 | + | 2.19133i | ||||
\(780\) | −7.53851 | + | 9.73398i | −0.269922 | + | 0.348532i | ||||
\(781\) | 11.5974 | + | 20.0872i | 0.414986 | + | 0.718777i | ||||
\(782\) | 1.00426i | 0.0359123i | ||||||||
\(783\) | −27.9000 | + | 23.9017i | −0.997064 | + | 0.854176i | ||||
\(784\) | 12.7539 | 0.455496 | ||||||||
\(785\) | −17.8197 | + | 10.2882i | −0.636011 | + | 0.367201i | ||||
\(786\) | 1.39020 | − | 0.0857295i | 0.0495867 | − | 0.00305787i | ||||
\(787\) | −21.3901 | − | 12.3496i | −0.762476 | − | 0.440216i | 0.0677081 | − | 0.997705i | \(-0.478431\pi\) |
−0.830184 | + | 0.557490i | \(0.811765\pi\) | |||||||
\(788\) | 42.2912 | + | 24.4168i | 1.50656 | + | 0.869814i | ||||
\(789\) | 19.9034 | − | 13.1882i | 0.708580 | − | 0.469511i | ||||
\(790\) | 1.16990 | + | 2.02633i | 0.0416232 | + | 0.0720936i | ||||
\(791\) | − | 9.70740i | − | 0.345155i | ||||||
\(792\) | 4.93554 | + | 6.53600i | 0.175377 | + | 0.232247i | ||||
\(793\) | −7.16731 | + | 8.16271i | −0.254519 | + | 0.289866i | ||||
\(794\) | −0.686872 | − | 1.18970i | −0.0243762 | − | 0.0422208i | ||||
\(795\) | 1.41960 | − | 2.85085i | 0.0503479 | − | 0.101109i | ||||
\(796\) | −9.40629 | + | 16.2922i | −0.333397 | + | 0.577461i | ||||
\(797\) | 6.15266 | − | 10.6567i | 0.217938 | − | 0.377480i | −0.736239 | − | 0.676721i | \(-0.763400\pi\) |
0.954178 | + | 0.299241i | \(0.0967335\pi\) | |||||||
\(798\) | 1.61365 | − | 3.24056i | 0.0571226 | − | 0.114715i | ||||
\(799\) | −2.10929 | + | 1.21780i | −0.0746212 | + | 0.0430826i | ||||
\(800\) | 1.98881i | 0.0703152i | ||||||||
\(801\) | −3.72035 | − | 30.0501i | −0.131452 | − | 1.06177i | ||||
\(802\) | −5.03213 | −0.177691 | ||||||||
\(803\) | 11.7863 | + | 20.4145i | 0.415930 | + | 0.720412i | ||||
\(804\) | −7.34676 | − | 11.0876i | −0.259100 | − | 0.391031i | ||||
\(805\) | 8.02364 | − | 13.8973i | 0.282796 | − | 0.489817i | ||||
\(806\) | −0.970957 | − | 2.86608i | −0.0342005 | − | 0.100953i | ||||
\(807\) | −1.77953 | − | 28.8570i | −0.0626423 | − | 1.01581i | ||||
\(808\) | −4.05880 | + | 2.34335i | −0.142788 | + | 0.0824386i | ||||
\(809\) | −46.5369 | −1.63615 | −0.818075 | − | 0.575112i | \(-0.804959\pi\) | ||||
−0.818075 | + | 0.575112i | \(0.804959\pi\) | |||||||
\(810\) | −1.47453 | + | 0.370791i | −0.0518097 | + | 0.0130283i | ||||
\(811\) | − | 36.6983i | − | 1.28865i | −0.764751 | − | 0.644326i | \(-0.777138\pi\) | ||
0.764751 | − | 0.644326i | \(-0.222862\pi\) | |||||||
\(812\) | 23.1242 | − | 13.3508i | 0.811500 | − | 0.468520i | ||||
\(813\) | 2.33568 | − | 0.144035i | 0.0819159 | − | 0.00505151i | ||||
\(814\) | 3.41525 | + | 1.97179i | 0.119704 | + | 0.0691113i | ||||
\(815\) | 7.81378 | − | 13.5339i | 0.273705 | − | 0.474070i | ||||
\(816\) | 3.92378 | − | 2.59993i | 0.137360 | − | 0.0910156i | ||||
\(817\) | 48.6618 | − | 28.0949i | 1.70246 | − | 0.982917i | ||||
\(818\) | 1.08811 | 0.0380449 | ||||||||
\(819\) | 17.1321 | + | 11.6549i | 0.598645 | + | 0.407256i | ||||
\(820\) | −21.5581 | −0.752842 | ||||||||
\(821\) | 4.82968 | − | 2.78842i | 0.168557 | − | 0.0973164i | −0.413348 | − | 0.910573i | \(-0.635641\pi\) |
0.581905 | + | 0.813257i | \(0.302307\pi\) | |||||||
\(822\) | 2.68142 | + | 1.33522i | 0.0935251 | + | 0.0465712i | ||||
\(823\) | 24.0011 | − | 41.5711i | 0.836625 | − | 1.44908i | −0.0560760 | − | 0.998427i | \(-0.517859\pi\) |
0.892701 | − | 0.450650i | \(-0.148808\pi\) | |||||||
\(824\) | −8.15985 | − | 4.71109i | −0.284262 | − | 0.164119i | ||||
\(825\) | 3.14156 | − | 6.30894i | 0.109375 | − | 0.219649i | ||||
\(826\) | −2.78819 | + | 1.60976i | −0.0970135 | + | 0.0560107i | ||||
\(827\) | 2.45866i | 0.0854961i | 0.999086 | + | 0.0427481i | \(0.0136113\pi\) | ||||
−0.999086 | + | 0.0427481i | \(0.986389\pi\) | |||||||
\(828\) | 29.8566 | + | 39.5383i | 1.03759 | + | 1.37405i | ||||
\(829\) | −24.7581 | −0.859885 | −0.429943 | − | 0.902856i | \(-0.641466\pi\) | ||||
−0.429943 | + | 0.902856i | \(0.641466\pi\) | |||||||
\(830\) | −0.511612 | + | 0.295380i | −0.0177583 | + | 0.0102528i | ||||
\(831\) | 11.5103 | − | 7.62685i | 0.399289 | − | 0.264572i | ||||
\(832\) | 8.47208 | + | 25.0080i | 0.293716 | + | 0.866995i | ||||
\(833\) | 1.18166 | − | 2.04670i | 0.0409421 | − | 0.0709138i | ||||
\(834\) | 3.37483 | − | 0.208116i | 0.116861 | − | 0.00720646i | ||||
\(835\) | −4.99304 | − | 8.64820i | −0.172791 | − | 0.299283i | ||||
\(836\) | −51.8092 | −1.79186 | ||||||||
\(837\) | −8.58040 | + | 24.3469i | −0.296582 | + | 0.841552i | ||||
\(838\) | 0.116822i | 0.00403556i | ||||||||
\(839\) | 0.862164 | − | 0.497770i | 0.0297652 | − | 0.0171849i | −0.485044 | − | 0.874490i | \(-0.661196\pi\) |
0.514809 | + | 0.857305i | \(0.327863\pi\) | |||||||
\(840\) | 2.22189 | − | 0.137018i | 0.0766626 | − | 0.00472756i | ||||
\(841\) | −10.4944 | + | 18.1769i | −0.361876 | + | 0.626788i | ||||
\(842\) | −2.90568 | + | 5.03278i | −0.100136 | + | 0.173441i | ||||
\(843\) | 23.2639 | + | 35.1096i | 0.801252 | + | 1.20924i | ||||
\(844\) | −8.90563 | − | 15.4250i | −0.306544 | − | 0.530951i | ||||
\(845\) | −12.8908 | + | 1.68114i | −0.443458 | + | 0.0578329i | ||||
\(846\) | 0.678061 | − | 1.60189i | 0.0233122 | − | 0.0550740i | ||||
\(847\) | 10.6459i | 0.365797i | ||||||||
\(848\) | −3.52075 | − | 6.09812i | −0.120903 | − | 0.209410i | ||||
\(849\) | 23.8417 | + | 11.8721i | 0.818245 | + | 0.407448i | ||||
\(850\) | 0.103821 | + | 0.0599413i | 0.00356104 | + | 0.00205597i | ||||
\(851\) | 41.6189 | + | 24.0287i | 1.42668 | + | 0.823693i | ||||
\(852\) | −8.67623 | + | 17.4238i | −0.297243 | + | 0.596928i | ||||
\(853\) | 13.6757 | − | 7.89568i | 0.468248 | − | 0.270343i | −0.247258 | − | 0.968950i | \(-0.579530\pi\) |
0.715506 | + | 0.698607i | \(0.246196\pi\) | |||||||
\(854\) | 0.975004 | 0.0333639 | ||||||||
\(855\) | 7.55253 | − | 17.8425i | 0.258291 | − | 0.610200i | ||||
\(856\) | 4.77096i | 0.163068i | ||||||||
\(857\) | 4.70055 | + | 8.14160i | 0.160568 | + | 0.278112i | 0.935072 | − | 0.354457i | \(-0.115334\pi\) |
−0.774505 | + | 0.632568i | \(0.782001\pi\) | |||||||
\(858\) | −0.579358 | + | 4.25365i | −0.0197790 | + | 0.145217i | ||||
\(859\) | 22.9738 | − | 39.7917i | 0.783855 | − | 1.35768i | −0.145826 | − | 0.989310i | \(-0.546584\pi\) |
0.929681 | − | 0.368366i | \(-0.120083\pi\) | |||||||
\(860\) | 14.8544 | + | 8.57616i | 0.506529 | + | 0.292445i | ||||
\(861\) | 2.23318 | + | 36.2135i | 0.0761066 | + | 1.23415i | ||||
\(862\) | −0.490765 | − | 0.850030i | −0.0167155 | − | 0.0289522i | ||||
\(863\) | 40.4470i | 1.37683i | 0.725317 | + | 0.688415i | \(0.241693\pi\) | ||||
−0.725317 | + | 0.688415i | \(0.758307\pi\) | |||||||
\(864\) | −3.43493 | + | 9.74661i | −0.116859 | + | 0.331586i | ||||
\(865\) | − | 16.0820i | − | 0.546804i | ||||||
\(866\) | 0.0201146 | − | 0.0116132i | 0.000683522 | − | 0.000394632i | ||||
\(867\) | 1.75865 | + | 28.5185i | 0.0597269 | + | 0.968538i | ||||
\(868\) | 9.38109 | − | 16.2485i | 0.318415 | − | 0.551511i | ||||
\(869\) | −48.8068 | − | 28.1786i | −1.65566 | − | 0.955895i | ||||
\(870\) | −1.72458 | + | 1.14272i | −0.0584689 | + | 0.0387420i | ||||
\(871\) | 2.74830 | − | 13.7728i | 0.0931224 | − | 0.466672i | ||||
\(872\) | −9.41633 | −0.318877 | ||||||||
\(873\) | 40.1550 | − | 30.3223i | 1.35904 | − | 1.02625i | ||||
\(874\) | 9.13983 | 0.309159 | ||||||||
\(875\) | −0.957814 | − | 1.65898i | −0.0323800 | − | 0.0560839i | ||||
\(876\) | −8.81759 | + | 17.7076i | −0.297919 | + | 0.598285i | ||||
\(877\) | 9.12386 | + | 5.26767i | 0.308091 | + | 0.177876i | 0.646072 | − | 0.763277i | \(-0.276411\pi\) |
−0.337981 | + | 0.941153i | \(0.609744\pi\) | |||||||
\(878\) | 4.92468 | + | 2.84327i | 0.166200 | + | 0.0959556i | ||||
\(879\) | 15.3536 | − | 30.8334i | 0.517865 | − | 1.03999i | ||||
\(880\) | −7.79142 | − | 13.4951i | −0.262649 | − | 0.454921i | ||||
\(881\) | −50.7372 | −1.70938 | −0.854690 | − | 0.519139i | \(-0.826253\pi\) | ||||
−0.854690 | + | 0.519139i | \(0.826253\pi\) | |||||||
\(882\) | 0.207383 | + | 1.67508i | 0.00698296 | + | 0.0564029i | ||||
\(883\) | 0.991413 | 0.0333637 | 0.0166818 | − | 0.999861i | \(-0.494690\pi\) | ||||
0.0166818 | + | 0.999861i | \(0.494690\pi\) | |||||||
\(884\) | 4.94666 | + | 0.987083i | 0.166374 | + | 0.0331992i | ||||
\(885\) | −14.3641 | + | 9.51775i | −0.482843 | + | 0.319936i | ||||
\(886\) | 0.924857 | + | 0.533966i | 0.0310712 | + | 0.0179390i | ||||
\(887\) | −25.7776 | + | 44.6481i | −0.865526 | + | 1.49913i | 0.000997961 | 1.00000i | \(0.499682\pi\) | |
−0.866524 | + | 0.499135i | \(0.833651\pi\) | |||||||
\(888\) | 0.410332 | + | 6.65399i | 0.0137698 | + | 0.223293i | ||||
\(889\) | −14.3444 | + | 8.28176i | −0.481097 | + | 0.277761i | ||||
\(890\) | − | 1.70511i | − | 0.0571555i | ||||||
\(891\) | 26.2922 | − | 25.4925i | 0.880823 | − | 0.854030i | ||||
\(892\) | 29.3533i | 0.982823i | ||||||||
\(893\) | 11.0832 | + | 19.1967i | 0.370887 | + | 0.642395i | ||||
\(894\) | 0.395945 | + | 6.42068i | 0.0132424 | + | 0.214740i | ||||
\(895\) | 5.78655 | + | 3.34086i | 0.193423 | + | 0.111673i | ||||
\(896\) | 4.99479 | − | 8.65123i | 0.166864 | − | 0.289017i | ||||
\(897\) | −7.06018 | + | 51.8359i | −0.235733 | + | 1.73075i | ||||
\(898\) | 0.211502 | + | 0.366333i | 0.00705793 | + | 0.0122247i | ||||
\(899\) | 35.1253i | 1.17150i | ||||||||
\(900\) | 5.86957 | − | 0.726682i | 0.195652 | − | 0.0242227i | ||||
\(901\) | −1.30480 | −0.0434693 | ||||||||
\(902\) | −6.50991 | + | 3.75850i | −0.216756 | + | 0.125144i | ||||
\(903\) | 12.8676 | − | 25.8409i | 0.428206 | − | 0.859930i | ||||
\(904\) | 2.94441 | + | 1.69995i | 0.0979295 | + | 0.0565396i | ||||
\(905\) | −10.5498 | − | 6.09096i | −0.350689 | − | 0.202470i | ||||
\(906\) | 0.0610168 | + | 0.0303836i | 0.00202715 | + | 0.00100943i | ||||
\(907\) | −2.35323 | − | 4.07591i | −0.0781377 | − | 0.135338i | 0.824309 | − | 0.566140i | \(-0.191564\pi\) |
−0.902446 | + | 0.430802i | \(0.858231\pi\) | |||||||
\(908\) | 32.2519i | 1.07032i | ||||||||
\(909\) | 12.6286 | + | 16.7237i | 0.418863 | + | 0.554689i | ||||
\(910\) | 0.876802 | + | 0.769880i | 0.0290657 | + | 0.0255213i | ||||
\(911\) | −4.21896 | − | 7.30746i | −0.139780 | − | 0.242107i | 0.787633 | − | 0.616145i | \(-0.211306\pi\) |
−0.927413 | + | 0.374038i | \(0.877973\pi\) | |||||||
\(912\) | −23.6621 | − | 35.7105i | −0.783530 | − | 1.18249i | ||||
\(913\) | 7.11461 | − | 12.3229i | 0.235459 | − | 0.407827i | ||||
\(914\) | 1.43690 | − | 2.48878i | 0.0475283 | − | 0.0823214i | ||||
\(915\) | 5.20842 | − | 0.321188i | 0.172185 | − | 0.0106182i | ||||
\(916\) | −3.97072 | + | 2.29250i | −0.131196 | + | 0.0757462i | ||||
\(917\) | 9.11856i | 0.301121i | ||||||||
\(918\) | 0.405273 | + | 0.473068i | 0.0133760 | + | 0.0156136i | ||||
\(919\) | −32.0996 | −1.05887 | −0.529434 | − | 0.848351i | \(-0.677596\pi\) | ||||
−0.529434 | + | 0.848351i | \(0.677596\pi\) | |||||||
\(920\) | 2.81019 | + | 4.86739i | 0.0926492 | + | 0.160473i | ||||
\(921\) | −3.53641 | + | 0.218080i | −0.116529 | + | 0.00718598i | ||||
\(922\) | −1.30948 | + | 2.26808i | −0.0431254 | + | 0.0746953i | ||||
\(923\) | −19.4658 | + | 6.59453i | −0.640725 | + | 0.217062i | ||||
\(924\) | −22.1880 | + | 14.7019i | −0.729931 | + | 0.483659i | ||||
\(925\) | 4.96822 | − | 2.86840i | 0.163354 | − | 0.0943125i | ||||
\(926\) | 6.19063 | 0.203437 | ||||||||
\(927\) | −16.4227 | + | 38.7979i | −0.539393 | + | 1.27429i | ||||
\(928\) | 14.0615i | 0.461590i | ||||||||
\(929\) | 34.1112 | − | 19.6941i | 1.11915 | − | 0.646142i | 0.177967 | − | 0.984036i | \(-0.443048\pi\) |
0.941184 | + | 0.337894i | \(0.109715\pi\) | |||||||
\(930\) | −0.647977 | + | 1.30128i | −0.0212480 | + | 0.0426706i | ||||
\(931\) | −18.6271 | − | 10.7544i | −0.610479 | − | 0.352460i | ||||
\(932\) | 8.36185 | − | 14.4832i | 0.273902 | − | 0.474411i | ||||
\(933\) | −35.1337 | − | 17.4950i | −1.15023 | − | 0.572760i | ||||
\(934\) | −1.48624 | + | 0.858083i | −0.0486313 | + | 0.0280773i | ||||
\(935\) | −2.88753 | −0.0944324 | ||||||||
\(936\) | −6.53529 | + | 3.15544i | −0.213613 | + | 0.103139i | ||||
\(937\) | −55.6528 | −1.81810 | −0.909050 | − | 0.416688i | \(-0.863191\pi\) | ||||
−0.909050 | + | 0.416688i | \(0.863191\pi\) | |||||||
\(938\) | −1.09168 | + | 0.630282i | −0.0356446 | + | 0.0205794i | ||||
\(939\) | 11.2048 | − | 7.42437i | 0.365653 | − | 0.242285i | ||||
\(940\) | −3.38324 | + | 5.85994i | −0.110349 | + | 0.191130i | ||||
\(941\) | 17.1215 | + | 9.88510i | 0.558145 | + | 0.322245i | 0.752401 | − | 0.658706i | \(-0.228896\pi\) |
−0.194256 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(942\) | −6.00940 | + | 0.370582i | −0.195797 | + | 0.0120742i | ||||
\(943\) | −79.3311 | + | 45.8018i | −2.58338 | + | 1.49151i | ||||
\(944\) | 38.0983i | 1.23999i | ||||||||
\(945\) | −1.82871 | − | 9.78447i | −0.0594879 | − | 0.318289i | ||||
\(946\) | 5.98076 | 0.194451 | ||||||||
\(947\) | −23.6649 | + | 13.6629i | −0.769006 | + | 0.443986i | −0.832520 | − | 0.553995i | \(-0.813103\pi\) |
0.0635141 | + | 0.997981i | \(0.479769\pi\) | |||||||
\(948\) | −2.91093 | − | 47.2040i | −0.0945426 | − | 1.53311i | ||||
\(949\) | −19.7830 | + | 6.70197i | −0.642182 | + | 0.217555i | ||||
\(950\) | 0.545529 | − | 0.944885i | 0.0176993 | − | 0.0306561i | ||||
\(951\) | −4.61297 | − | 6.96183i | −0.149586 | − | 0.225753i | ||||
\(952\) | −0.456024 | − | 0.789857i | −0.0147798 | − | 0.0255994i | ||||
\(953\) | 38.3958 | 1.24376 | 0.621881 | − | 0.783112i | \(-0.286369\pi\) | ||||
0.621881 | + | 0.783112i | \(0.286369\pi\) | |||||||
\(954\) | 0.743670 | − | 0.561569i | 0.0240772 | − | 0.0181815i | ||||
\(955\) | 16.5268i | 0.534795i | ||||||||
\(956\) | −15.4406 | + | 8.91465i | −0.499386 | + | 0.288320i | ||||
\(957\) | 22.2117 | − | 44.6060i | 0.718003 | − | 1.44191i | ||||
\(958\) | −0.541899 | + | 0.938596i | −0.0175079 | + | 0.0303247i | ||||
\(959\) | −9.80527 | + | 16.9832i | −0.316629 | + | 0.548417i | ||||
\(960\) | 5.65391 | − | 11.3543i | 0.182479 | − | 0.366458i | ||||
\(961\) | −3.15935 | − | 5.47216i | −0.101915 | − | 0.176521i | ||||
\(962\) | −2.30559 | + | 2.62579i | −0.0743352 | + | 0.0846590i | ||||
\(963\) | 21.1713 | − | 2.62112i | 0.682237 | − | 0.0844643i | ||||
\(964\) | 16.6544i | 0.536403i | ||||||||
\(965\) | 7.19271 | + | 12.4581i | 0.231542 | + | 0.401042i | ||||
\(966\) | 3.91426 | − | 2.59362i | 0.125939 | − | 0.0834483i | ||||
\(967\) | −28.9525 | − | 16.7157i | −0.931050 | − | 0.537542i | −0.0439066 | − | 0.999036i | \(-0.513980\pi\) |
−0.887144 | + | 0.461494i | \(0.847314\pi\) | |||||||
\(968\) | −3.22907 | − | 1.86430i | −0.103786 | − | 0.0599209i | ||||
\(969\) | −7.92301 | + | 0.488589i | −0.254524 | + | 0.0156957i | ||||
\(970\) | 2.45389 | − | 1.41675i | 0.0787896 | − | 0.0454892i | ||||
\(971\) | −29.0853 | −0.933391 | −0.466695 | − | 0.884418i | \(-0.654556\pi\) | ||||
−0.466695 | + | 0.884418i | \(0.654556\pi\) | |||||||
\(972\) | 30.0202 | + | 6.57621i | 0.962897 | + | 0.210932i | ||||
\(973\) | 22.1361i | 0.709651i | ||||||||
\(974\) | −1.75446 | − | 3.03881i | −0.0562165 | − | 0.0973699i | ||||
\(975\) | 4.93745 | + | 3.82382i | 0.158125 | + | 0.122460i | ||||
\(976\) | 5.76886 | − | 9.99196i | 0.184657 | − | 0.319835i | ||||
\(977\) | 34.5714 | + | 19.9598i | 1.10604 | + | 0.638570i | 0.937800 | − | 0.347176i | \(-0.112859\pi\) |
0.168236 | + | 0.985747i | \(0.446193\pi\) | |||||||
\(978\) | 3.81188 | − | 2.52578i | 0.121890 | − | 0.0807656i | ||||
\(979\) | 20.5350 | + | 35.5676i | 0.656300 | + | 1.13675i | ||||
\(980\) | − | 6.56569i | − | 0.209733i | ||||||
\(981\) | 5.17323 | + | 41.7854i | 0.165169 | + | 1.33410i | ||||
\(982\) | 0.659574i | 0.0210478i | ||||||||
\(983\) | 7.79123 | − | 4.49827i | 0.248502 | − | 0.143473i | −0.370576 | − | 0.928802i | \(-0.620840\pi\) |
0.619078 | + | 0.785330i | \(0.287506\pi\) | |||||||
\(984\) | −11.3752 | − | 5.66433i | −0.362628 | − | 0.180572i | ||||
\(985\) | 12.3852 | − | 21.4517i | 0.394624 | − | 0.683509i | ||||
\(986\) | 0.734046 | + | 0.423802i | 0.0233768 | + | 0.0134966i | ||||
\(987\) | 10.1940 | + | 5.07616i | 0.324480 | + | 0.161576i | ||||
\(988\) | 8.98351 | − | 45.0198i | 0.285803 | − | 1.43227i | ||||
\(989\) | 72.8828 | 2.31754 | ||||||||
\(990\) | 1.64574 | − | 1.24275i | 0.0523051 | − | 0.0394972i | ||||
\(991\) | −24.4591 | −0.776967 | −0.388484 | − | 0.921456i | \(-0.627001\pi\) | ||||
−0.388484 | + | 0.921456i | \(0.627001\pi\) | |||||||
\(992\) | 4.94024 | + | 8.55674i | 0.156853 | + | 0.271677i | ||||
\(993\) | 22.2602 | + | 33.5948i | 0.706406 | + | 1.06610i | ||||
\(994\) | 1.59757 | + | 0.922358i | 0.0506719 | + | 0.0292554i | ||||
\(995\) | 8.26402 | + | 4.77123i | 0.261987 | + | 0.151258i | ||||
\(996\) | 11.9182 | − | 0.734959i | 0.377642 | − | 0.0232881i | ||||
\(997\) | −0.419322 | − | 0.726287i | −0.0132801 | − | 0.0230017i | 0.859309 | − | 0.511457i | \(-0.170894\pi\) |
−0.872589 | + | 0.488455i | \(0.837561\pi\) | |||||||
\(998\) | 0.567761 | 0.0179722 | ||||||||
\(999\) | 29.3019 | − | 5.47650i | 0.927072 | − | 0.173269i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 585.2.bt.b.571.26 | yes | 108 | |
9.7 | even | 3 | inner | 585.2.bt.b.376.29 | yes | 108 | |
13.12 | even | 2 | inner | 585.2.bt.b.571.29 | yes | 108 | |
117.25 | even | 6 | inner | 585.2.bt.b.376.26 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.bt.b.376.26 | ✓ | 108 | 117.25 | even | 6 | inner | |
585.2.bt.b.376.29 | yes | 108 | 9.7 | even | 3 | inner | |
585.2.bt.b.571.26 | yes | 108 | 1.1 | even | 1 | trivial | |
585.2.bt.b.571.29 | yes | 108 | 13.12 | even | 2 | inner |